Theorem bj-cbveximi

Description: An equality-free general instance of one half of a precise form of bj-cbvex . (Contributed by BJ, 12-Mar-2023) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	bj-cbvalimi.maj	|- ( ch -> ( ph -> ps ) )
	bj-cbveximi.denote	|- A. x E. y ch
Assertion	bj-cbveximi	|- ( E. x ph -> E. y ps )

Proof

Step	Hyp	Ref	Expression
1		bj-cbvalimi.maj	|- ( ch -> ( ph -> ps ) )
2		bj-cbveximi.denote	|- A. x E. y ch
3	1	gen2	|- A. x A. y ( ch -> ( ph -> ps ) )
4		bj-cbvexim	|- ( A. x E. y ch -> ( A. x A. y ( ch -> ( ph -> ps ) ) -> ( E. x ph -> E. y ps ) ) )
5	2 3 4	mp2	|- ( E. x ph -> E. y ps )