Theorem exlimim

Description: Closed form of exlimimd . (Contributed by ML, 17-Jul-2020)

	Ref	Expression
Assertion	exlimim	|- ( ( E. x ph /\ A. x ( ph -> ps ) ) -> ps )

Proof

Step	Hyp	Ref	Expression
1		nfa1	|- F/ x A. x ( ph -> ps )
2		nfv	|- F/ x ps
3		sp	|- ( A. x ( ph -> ps ) -> ( ph -> ps ) )
4	1 2 3	exlimd	|- ( A. x ( ph -> ps ) -> ( E. x ph -> ps ) )
5	4	impcom	|- ( ( E. x ph /\ A. x ( ph -> ps ) ) -> ps )