Theorem bj-equsal1

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

	Ref	Expression
Hypotheses	bj-equsal1.1	|- F/ x ps
	bj-equsal1.2	|- ( x = y -> ( ph -> ps ) )
Assertion	bj-equsal1	|- ( A. x ( x = y -> ph ) -> ps )

Proof

Step	Hyp	Ref	Expression
1		bj-equsal1.1	|- F/ x ps
2		bj-equsal1.2	|- ( x = y -> ( ph -> ps ) )
3	2	a2i	|- ( ( x = y -> ph ) -> ( x = y -> ps ) )
4	3	alimi	|- ( A. x ( x = y -> ph ) -> A. x ( x = y -> ps ) )
5	1	bj-equsal1ti	|- ( A. x ( x = y -> ps ) <-> ps )
6	4 5	sylib	|- ( A. x ( x = y -> ph ) -> ps )