Theorem bj-ceqsal

Description: Remove from ceqsal dependency on ax-ext (and on df-cleq , df-v , df-clab , df-sb ). (Contributed by BJ, 12-Oct-2019) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-ceqsal.1	|- F/ x ps
	bj-ceqsal.2	|- A e. _V
	bj-ceqsal.3	|- ( x = A -> ( ph <-> ps ) )
Assertion	bj-ceqsal	|- ( A. x ( x = A -> ph ) <-> ps )

Proof

Step	Hyp	Ref	Expression
1		bj-ceqsal.1	|- F/ x ps
2		bj-ceqsal.2	|- A e. _V
3		bj-ceqsal.3	|- ( x = A -> ( ph <-> ps ) )
4	1 3	bj-ceqsalgv	|- ( A e. _V -> ( A. x ( x = A -> ph ) <-> ps ) )
5	2 4	ax-mp	|- ( A. x ( x = A -> ph ) <-> ps )