Theorem bj-cbvalimi

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

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

Proof

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