Theorem cbvrabv2w

Description: A more general version of cbvrabv . Version of cbvrabv2 with a disjoint variable condition, which does not require ax-13 . (Contributed by Glauco Siliprandi, 23-Oct-2021) (Revised by Gino Giotto, 16-Apr-2024)

	Ref	Expression
Hypotheses	cbvrabv2w.1	|- ( x = y -> A = B )
	cbvrabv2w.2	|- ( x = y -> ( ph <-> ps ) )
Assertion	cbvrabv2w	|- { x e. A | ph } = { y e. B | ps }

Proof

Step	Hyp	Ref	Expression
1		cbvrabv2w.1	|- ( x = y -> A = B )
2		cbvrabv2w.2	|- ( x = y -> ( ph <-> ps ) )
3		nfcv	|- F/_ y A
4		nfcv	|- F/_ x B
5		nfv	|- F/ y ph
6		nfv	|- F/ x ps
7	3 4 5 6 1 2	cbvrabcsfw	|- { x e. A | ph } = { y e. B | ps }