Theorem ceqsralvOLD

Description: Obsolete version of ceqsalv as of 8-Sep-2024. (Contributed by NM, 21-Jun-2013) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypothesis	ceqsralv.2	|- ( x = A -> ( ph <-> ps ) )
Assertion	ceqsralvOLD	|- ( A e. B -> ( A. x e. B ( x = A -> ph ) <-> ps ) )

Proof

Step	Hyp	Ref	Expression
1		ceqsralv.2	|- ( x = A -> ( ph <-> ps ) )
2		nfv	|- F/ x ps
3	1	ax-gen	|- A. x ( x = A -> ( ph <-> ps ) )
4		ceqsralt	|- ( ( F/ x ps /\ A. x ( x = A -> ( ph <-> ps ) ) /\ A e. B ) -> ( A. x e. B ( x = A -> ph ) <-> ps ) )
5	2 3 4	mp3an12	|- ( A e. B -> ( A. x e. B ( x = A -> ph ) <-> ps ) )