Theorem bj-cbvex2vv

Description: Version of cbvex2vv 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-cbval2vv.1	|- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )
Assertion	bj-cbvex2vv	|- ( E. x E. y ph <-> E. z E. w ps )

Proof

Step	Hyp	Ref	Expression
1		bj-cbval2vv.1	|- ( ( x = z /\ y = w ) -> ( ph <-> ps ) )
2		nfv	|- F/ z ph
3		nfv	|- F/ w ph
4		nfv	|- F/ x ps
5		nfv	|- F/ y ps
6	2 3 4 5 1	cbvex2v	|- ( E. x E. y ph <-> E. z E. w ps )