Theorem bj-aleximiALT

Description: Alternate proof of aleximi from exim , which is sometimes used as an axiom in instuitionistic modal logic. (Contributed by BJ, 9-Dec-2023) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	bj-aleximiALT.1	|- ( ph -> ( ps -> ch ) )
Assertion	bj-aleximiALT	|- ( A. x ph -> ( E. x ps -> E. x ch ) )

Proof

Step	Hyp	Ref	Expression
1		bj-aleximiALT.1	|- ( ph -> ( ps -> ch ) )
2	1	alimi	|- ( A. x ph -> A. x ( ps -> ch ) )
3		bj-eximALT	|- ( A. x ( ps -> ch ) -> ( E. x ps -> E. x ch ) )
4	2 3	syl	|- ( A. x ph -> ( E. x ps -> E. x ch ) )