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WASHINGTON (CNN) — In a dramatic ruling, the Supreme Court on Monday threw out a Texas abortion access law in a victory to supporters of abortion rights who argued it would have shuttered all but a handful of clinics in the state.

The 5-3 ruling is the most significant decision from the Supreme Court on abortion in two decades and could serve to deter other states from passing so-called “clinic shutdown” laws.

In joining with the liberal justices, perennial swing vote Justice Anthony Kennedy helped deliver a victory to abortion rights activists and signaled the court’s majority in their favor could continue regardless of the presidential election and the filling of the empty seat on the bench left by the death of conservative Justice Antonin Scalia.

Justice Stephen Breyer wrote the majority opinion, which was joined in full by Kennedy. Breyer wrote that despite arguments that the restrictions were designed to protect women’s health, the reality is that they merely amounted to burdening women who seek abortions.

“There was no significant health-related problem that the new law helped to cure,” Breyer wrote. “We agree with the District Court that the surgical-center requirement, like the admitting-privileges requirement, provides few, if any, health benefits for women, poses a substantial obstacle to women seeking abortions, and constitutes an “undue burden” on their constitutional right to do so.”

Justice Ruth Bader Ginsburg joined Breyer’s opinion and wrote a brief concurring opinion, which focused on what she called women in “desperate circumstances.”

“When a State severely limits access to safe and legal procedures, women in desperate circumstances may resort to unlicensed rogue practitioners, faute de mieux, at great risk to their health and safety,” she wrote.

“My office and I will be carefully reviewing the impact of the opinion, if any, on the Louisiana’s admitting privileges law; however, we remain committed to enforcing our state’s pro-life and pro-woman laws.” — Louisiana Atty. Gen. Jeff Landry

Political implications

The ruling will have reverberations on the presidential election, where the fate of the Supreme Court has been front-and-center after the death of Scalia in February. Senate Republicans have refused to act on President Barack Obama’s nomination of Judge Merrick Garland, leaving the court with eight justices.

But Monday’s ruling signals that even if Republicans were to name that replacement, the court still has a five-justice majority that could rule against abortion restrictions. And if Hillary Clinton were to win, the majority could even grow.

Hillary Clinton immediately praised the ruling.

“SCOTUS’s decision is a victory for women in Texas and across America. Safe abortion should be a right—not just on paper, but in reality. -H”

President Barack Obama said he is “pleased” by the ruling.

“We remain strongly committed to the protection of women’s health, including protecting a woman’s access to safe, affordable health care and her right to determine her own future, the President said.

The court’s decision has major implications for the future political battles over abortion beyond Texas.

Anti-abortion activists since Roe v. Wade have worked to pass a slew of laws across the country restricting abortions or making them more difficult, like the law struck down in Texas.

But Monday’s ruling strengthened the premise of the 1992 case Planned Parenthood v Casey, sending a message to states that might pass such laws and lower courts that would uphold them that they have a high hurdle to prove they’re constitutional. The Casey ruling said that states could impose restrictions as long as they didn’t impose an undue burden on the woman.

“By clarifying exactly what the ‘undue burden’ test requires, I suspect the majority was hoping to dissuade states like Oklahoma from continuing to pass laws that so directly challenge the central premise of Roe v. Wade — that the Constitution protects a pregnant woman’s right to an abortion in a meaningful percentage of cases,” said Steve Vladeck, CNN contributor and professor of law at American University Washington College of Law.

“In the process, the Court today has called into question everything from categorical bans on abortions to so-called ‘fetal heartbeat’ restrictions, and perhaps plenty of other laws in between,” Vladeck added.

Already, both sides signaled they intend to keep fighting.

“Our fight is far from over,” Clinton said in a statement. “In Texas and across the country, a woman’s constitutional right to make her own health decisions is under attack. In the first three months of 2016, states introduced more than 400 measures restricting access to abortion.”

Texas Gov. Greg Abbott decried the ruling. “The decision erodes States’ lawmaking authority to safeguard the health and safety of women and subjects more innocent life to being lost,” the Republican governor said in a statement. “Texas’ goal is to protect innocent life, while ensuring the highest health and safety standards for women.”

“I’m disappointed in the Court’s decision. But our fight to protect women’s health & promote life will not stop here,” House Speaker Paul Ryan tweeted.

Kennedy the swing vote

All eyes were on Kennedy entering oral arguments — a position the 79-year-old justice has often found himself in on the abortion issue.

Kennedy was one of the authors of Casey, but then disappointed supporters of abortion rights when he upheld the federal partial birth abortion ban in 2007. All eyes were on him for this case to see if he would take the opportunity to clarify Casey. Instead, as the most senior justice in the majority it was his choice to allow Breyer to write.

“The fact that Justice Kennedy gave away this opinion assignment and didn’t write separately is striking,” said Vladeck. “Kennedy has not only been the swing vote on abortion issues since he joined the Court in 1988, but he has written an opinion in virtually every major abortion case during that time, including the majority opinion in the Court’s controversial 2007 decision upholding the federal ban on so-called ‘partial-birth’ abortions.

“It’s not stunning that he sided with the liberals in striking down the Texas law in this case, but it is stunning that he didn’t feel the need to explain why,” Vladeck added.

Strong dissents from Thomas, Alito

Justices Clarence Thomas and Samuel Alito wrote dissents.

Thomas wrote a bitter dissent for himself, accusing the court of eroding the Constitution.

“The Court has simultaneously transformed judicially created rights like the right to abortion into preferred constitutional rights, while disfavoring many of the rights actually enumerated in the Constitution,” Thomas wrote. “But our Constitution renounces the notion that some constitutional rights are more equal than others. … A law either infringes a constitutional right, or not; there is no room for the judiciary to invent tolerable degrees of encroachment. Unless the Court abides by one set of rules to adjudicate constitutional rights, it will continue reducing constitutional law to policy-driven value judgments until the last shreds of its legitimacy disappear.”

While Thomas would have upheld the laws, in Alito’s dissent, joined by Chief Justice John Roberts, the justices would have sent the laws back to the lower courts to be decided after more evidence was presented.

Alito accused the justices in the majority of fabricating claims for the attorneys in the case.

“Determined to strike down two provisions of a new Texas abortion statute in all of their applications, the Court simply disregards basic rules that apply in all other cases,” Alito wrote. “The Court favors petitioners with a victory that they did not have the audacity to seek.”

Alito thought the two provisions of the law should have been dealt with separately and he condemns the majority for failing to do that analysis.

“If some applications are unconstitutional, the severability clause plainly requires that those applications be severed and that the rest be left intact….How can the Court possibly escape this painfully obvious conclusion. Its main argument is that it need not honor the severability provision because doing so would be too burdensome.”

Carrie Severino, chief counsel and policy director of the Judicial Crisis Network and former clerk to Thomas, said the ruling “made clear that some constitutional rights are more equal than others.” In a statement, she added that “by throwing out the regular legal rules in order to carry water for the abortion industry, the Court has further threatened its own legitimacy. It’s no wonder the Supreme Court is suffering record levels of disapproval with the American people.”

Impact of the law

There were two provisions of the law at issue. The first said that doctors have to have locl admitting privileges at nearby hospitals, the second says that the clinics have to upgrade their facilities to hospital-like standards.

Critics say if the 2013 law, known as H.B. 2, is allowed to go into effect it could shutter all but a handful of clinics in a state with 5.4 million women of reproductive age.

Texas countered that the law was passed in response to the Kermit Gosnell scandal. The Pennsylvania man was convicted in 2013 of first-degree murder for killing babies that were born alive in his clinic.

State Solicitor General Scott Keller argued in court papers that if the court were to uphold the law, an abortion clinic “will remain open in each area where one will close, meaning that over 90% of Texas women of reproductive age will live within 150 miles of an open abortion clinic.”

A federal appeals court upheld the Texas law in 2015, and last spring a majority of the Supreme Court voted to stay that ruling pending appeal. The four conservative justices at the time: John Roberts, along with Thomas, Alito and the late Justice Antonin Scalia, publicly noted that they would have denied the stay.