Theorem rexbidvaALT

Description: Alternate proof of rexbidva , shorter but requires more axioms. (Contributed by NM, 9-Mar-1997) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	rexbidvaALT.1	|- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )
Assertion	rexbidvaALT	|- ( ph -> ( E. x e. A ps <-> E. x e. A ch ) )

Proof

Step	Hyp	Ref	Expression
1		rexbidvaALT.1	|- ( ( ph /\ x e. A ) -> ( ps <-> ch ) )
2		nfv	|- F/ x ph
3	2 1	rexbida	|- ( ph -> ( E. x e. A ps <-> E. x e. A ch ) )