Theorem bj-ceqsalg

Description: Remove from ceqsalg dependency on ax-ext (and on df-cleq and df-v ). See also bj-ceqsalgv . (Contributed by BJ, 12-Oct-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-ceqsalg.1	|- F/ x ps
	bj-ceqsalg.2	|- ( x = A -> ( ph <-> ps ) )
Assertion	bj-ceqsalg	|- ( 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		bj-elisset	|- ( A e. V -> E. x x = A )
4	1 2	bj-ceqsalg0	|- ( E. x x = A -> ( A. x ( x = A -> ph ) <-> ps ) )
5	3 4	syl	|- ( A e. V -> ( A. x ( x = A -> ph ) <-> ps ) )