**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.