SAN FRANCISCO -- Supporters of California's gay marriage ban have filed an appeal of a federal judge's ruling to strike down the voter-approved law.

On Wednesday, a federal judge in San Francisco overturned California's Proposition 8, which restricts a marriage to one man and one woman. U.S. District Judge Vaughn Walker ruled the law violates federal equal protections and due process laws.

Thursday’s appeal to the 9th U.S. Circuit Court of Appeals was expected, as lawyers on both sides of the legal battle repeatedly vowed to carry the fight to a higher court if they lost. Attorney Andrew Pugno of ProtectMarriage.com said overturning the voter-backed initiative “short-circuits the democratic process.”

The 9th Circuit court has no deadlines to hear the case, which will be randomly assigned to a three-judge panel.

Also on Thursday, the Mexican Supreme Court voted to uphold the constitutionality of Mexico City's 6-month-old law allowing same-sex marriages.

The justices voted 8-2 to uphold the law against challenges filed by federal prosecutors, who argued it violates the constitutional principle of protection of the family. Justices on the majority side argued that nowhere does the constitution define what a family is.

Hundreds of couples have been married so far under the law, the first of its kind to be enacted in Latin America.