Theorem bj-equsal

Description: Shorter proof of equsal . (Contributed by BJ, 30-Sep-2018) Proof modification is discouraged to avoid using equsal , but "min */exc equsal" is ok. (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-equsal.1	|- F/ x ps
	bj-equsal.2	|- ( x = y -> ( ph <-> ps ) )
Assertion	bj-equsal	|- ( A. x ( x = y -> ph ) <-> ps )

Proof

Step	Hyp	Ref	Expression
1		bj-equsal.1	|- F/ x ps
2		bj-equsal.2	|- ( x = y -> ( ph <-> ps ) )
3	2	biimpd	|- ( x = y -> ( ph -> ps ) )
4	1 3	bj-equsal1	|- ( A. x ( x = y -> ph ) -> ps )
5	2	biimprd	|- ( x = y -> ( ps -> ph ) )
6	1 5	bj-equsal2	|- ( ps -> A. x ( x = y -> ph ) )
7	4 6	impbii	|- ( A. x ( x = y -> ph ) <-> ps )