Theorem bj-exalimsi

Description: An inference for distributing quantifiers over a nested implication. (Almost) the general statement that spimfw proves. (Contributed by BJ, 29-Sep-2019)

	Ref	Expression
Hypotheses	bj-exalimsi.1	|- ( ph -> ( ps -> ch ) )
	bj-exalimsi.2	|- ( E. x ph -> ( -. ch -> A. x -. ch ) )
Assertion	bj-exalimsi	|- ( E. x ph -> ( A. x ps -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		bj-exalimsi.1	|- ( ph -> ( ps -> ch ) )
2		bj-exalimsi.2	|- ( E. x ph -> ( -. ch -> A. x -. ch ) )
3	2	bj-exalims	|- ( A. x ( ph -> ( ps -> ch ) ) -> ( E. x ph -> ( A. x ps -> ch ) ) )
4	3 1	mpg	|- ( E. x ph -> ( A. x ps -> ch ) )