“Almost all Texas hospitals required that for a doctor to maintain privileges there, he or she had to admit a minimum number of patients annually,” Judge Jerry E. Smith wrote in the opinion joined by Judge Edith Brown Clement. “Few Louisiana hospitals made that demand.” Smith wrote that there is no evidence that any Louisiana clinics will close because of the law.

Supporters of the law said abortion doctors need to be able to admit patients to a hospital within 30 miles (50 kilometers) in case of medical complications. Opponents said the law would make it very difficult or impossible for many women to obtain abortions — a contention the appeals court majority rejected.

The majority didn’t find fault with the district judge’s decision that the law’s benefits were minimal. But Smith wrote that the 2017 ruling, by Judge John deGravelles, overstated the burden on women seeking an abortion.

Opponents of the law argued the law would eventually result in loss of access to abortion by 70 percent of women seeking the procedure in Louisiana. Smith’s opinion said there is one doctor at one clinic who currently is unable to obtain admitting privileges. If he stops performing the procedure, Smith wrote, it would affect “at most, only 30 percent of women, and even then, not substantially.

The dissenting judge, Patrick Higginbotham, agreed with the law’s opponents who said the law substantially burdens women’s abortion access while having “no demonstrable medical benefit.”