By rejecting a Texas abortion law Monday, the Supreme Court has set in motion a reshaping of the legal landscape across dozens of states where similar attempts to impose debatable medical requirements on clinics and providers are now in jeopardy.

The demands of those laws — that clinics meet hospital standards and doctors obtain admitting privileges at nearby hospitals — had been among the most potent tools of abortion opponents in recent years, shuttering providers and reducing access in the name of improved health.

The majority of justices said those requirements overstepped the state's interest in protecting women's health, instead imposing undue burdens on their constitutional rights.

The ruling may doom similar restrictions in other states, including Mississippi, Louisiana and Wisconsin. The justices may act Tuesday on appeals of rulings that struck down admitting-privileges rules in Mississippi and Wisconsin. GOP lawmakers' push to legislate the industry out of existence in those places and others has helped reduce abortion access at a rapid rate. Since 2011, at least 162 providers have shut or stopped offering the procedure, while just 21 opened.

Monday's ruling put abortion-rights supporters in an unfamiliar place: on the side of victory.

"We won! Our clinics stay open!" proclaims a banner hanging outside the Austin clinic location of Whole Woman's Health, the lead plaintiff challenging the law.

The court ruled that neither of the major provisions at issue in Texas House Bill 2, passed in 2013, "offers medical benefits sufficient to justify the burdens upon access that each imposes." The law 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."

That strikes at the heart of why proponents of the Texas law and others like it said the provisions were necessary: to protect women's health and raise the standards of abortion care, which they claimed is dangerously low.

Ever since 1973, when the Supreme Court made abortion legal across the U.S., those who consider the procedure equivalent to murder have sought ways to limit it, including waiting periods, graphic lectures, parental consent and banning of certain kinds of abortions as unduly cruel to the fetus.

All have had some success but few proved as potent as the Texas limits, which expropriated the phrase "reproductive health" from abortion-rights advocates. Foes of the procedure admitted defeat but vowed to push ahead in courts and legislatures.

Clarke Forsythe, senior counsel at Americans United for Life, said the group doesn't "read today's decision as foreclosing all clinic regulations and admitting privilege requirements, but it clearly puts a greater burden on the states to give the justices more evidence."

He added, "There are dozens of investigations ongoing across the country into abortion clinic scandals and substandard conditions and providers. And the states will move ahead with trying to fill that vacuum, but the justices have no doubt made it harder to protect women's health."

Officials at Planned Parenthood and its political action fund vowed to redouble efforts to both restore access and fight "state by state, legislature by legislature, law by law."