Theorem bj-equsal2

Description: One direction of equsal . (Contributed by BJ, 30-Sep-2018)

	Ref	Expression
Hypotheses	bj-equsal2.1	|- F/ x ph
	bj-equsal2.2	|- ( x = y -> ( ph -> ps ) )
Assertion	bj-equsal2	|- ( ph -> A. x ( x = y -> ps ) )

Proof

Step	Hyp	Ref	Expression
1		bj-equsal2.1	|- F/ x ph
2		bj-equsal2.2	|- ( x = y -> ( ph -> ps ) )
3	1	bj-equsal1ti	|- ( A. x ( x = y -> ph ) <-> ph )
4	2	a2i	|- ( ( x = y -> ph ) -> ( x = y -> ps ) )
5	4	alimi	|- ( A. x ( x = y -> ph ) -> A. x ( x = y -> ps ) )
6	3 5	sylbir	|- ( ph -> A. x ( x = y -> ps ) )