ATLANTA — A federal judge in Georgia has ruled that the state’s constitutional ban on same-sex marriage cannot be enforced.

The ruling is effectively a formality. State probate courts have been issuing marriage licenses to same-sex couples since a June 26 U.S. Supreme Court ruling legalized same-sex marriage nationwide.

Georgia’s constitution prohibits same-sex marriage and says the state will recognize only the union of a man and a woman as marriage and that same-sex marriages performed in others states are not legally recognized.

In April 2014, gay-rights group Lambda Legal filed a lawsuit challenging that ban on behalf of three couples and a widow.

U.S. District Judge William Duffey on Wednesday signed an order ruling in their favor and saying the Supreme Court ruling means the same-sex marriage ban can’t be enforced.

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