Theorem bj-ceqsalg0

Description: The FOL content of ceqsalg . (Contributed by BJ, 12-Oct-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-ceqsalg0.1	|- F/ x ps
	bj-ceqsalg0.2	|- ( ch -> ( ph <-> ps ) )
Assertion	bj-ceqsalg0	|- ( E. x ch -> ( A. x ( ch -> ph ) <-> ps ) )

Proof

Step	Hyp	Ref	Expression
1		bj-ceqsalg0.1	|- F/ x ps
2		bj-ceqsalg0.2	|- ( ch -> ( ph <-> ps ) )
3	2	ax-gen	|- A. x ( ch -> ( ph <-> ps ) )
4		bj-ceqsalt0	|- ( ( F/ x ps /\ A. x ( ch -> ( ph <-> ps ) ) /\ E. x ch ) -> ( A. x ( ch -> ph ) <-> ps ) )
5	1 3 4	mp3an12	|- ( E. x ch -> ( A. x ( ch -> ph ) <-> ps ) )