Theorem cbvrabv2

Description: A more general version of cbvrabv . Usage of this theorem is discouraged because it depends on ax-13 . Use of cbvrabv2w is preferred. (Contributed by Glauco Siliprandi, 23-Oct-2021) (New usage is discouraged.)

	Ref	Expression
Hypotheses	cbvrabv2.1	|- ( x = y -> A = B )
	cbvrabv2.2	|- ( x = y -> ( ph <-> ps ) )
Assertion	cbvrabv2	|- { x e. A | ph } = { y e. B | ps }

Proof

Step	Hyp	Ref	Expression
1		cbvrabv2.1	|- ( x = y -> A = B )
2		cbvrabv2.2	|- ( 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	cbvrabcsf	|- { x e. A | ph } = { y e. B | ps }