Theorem bj-ceqsalgALT

Description: Alternate proof of bj-ceqsalg . (Contributed by BJ, 12-Oct-2019) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	bj-ceqsalg.1	|- F/ x ps
	bj-ceqsalg.2	|- ( x = A -> ( ph <-> ps ) )
Assertion	bj-ceqsalgALT	|- ( A e. V -> ( A. x ( x = A -> ph ) <-> ps ) )

Proof

Step	Hyp	Ref	Expression
1		bj-ceqsalg.1	|- F/ x ps
2		bj-ceqsalg.2	|- ( x = A -> ( ph <-> ps ) )
3	2	ax-gen	|- A. x ( x = A -> ( ph <-> ps ) )
4		bj-ceqsalt	|- ( ( F/ x ps /\ A. x ( x = A -> ( ph <-> ps ) ) /\ A e. V ) -> ( A. x ( x = A -> ph ) <-> ps ) )
5	1 3 4	mp3an12	|- ( A e. V -> ( A. x ( x = A -> ph ) <-> ps ) )