Theorem: Let V be the set of valid arguments against marriage equality. Then V is empty.
Proof: Let P be a valid argument. Then, by now, someone would have argued P. This has not occurred. (Proof: by exhaustion.) By contradiction, it follows that P does not exist, and thus V is empty. QED.
An alternative, direct proof of the theorem was provided by the California Supreme Court; their proof applied the definition of equality.
Consideration of the many straight-forward corollaries of this theorem are left to the reader.