Theorem bj-cbvaldvav

Description: Version of cbvaldva with a disjoint variable condition, which does not require ax-13 . (Contributed by BJ, 16-Jun-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	bj-cbvaldvav.1	|- ( ( ph /\ x = y ) -> ( ps <-> ch ) )
Assertion	bj-cbvaldvav	|- ( ph -> ( A. x ps <-> A. y ch ) )

Proof

Step	Hyp	Ref	Expression
1		bj-cbvaldvav.1	|- ( ( ph /\ x = y ) -> ( ps <-> ch ) )
2		nfv	|- F/ y ph
3		nfvd	|- ( ph -> F/ y ps )
4	1	ex	|- ( ph -> ( x = y -> ( ps <-> ch ) ) )
5	2 3 4	bj-cbvaldv	|- ( ph -> ( A. x ps <-> A. y ch ) )