Theorem r19.29a

Description: A commonly used pattern in the spirit of r19.29 . (Contributed by Thierry Arnoux, 22-Nov-2017) Reduce axiom usage. (Revised by Wolf Lammen, 17-Jun-2023)

	Ref	Expression
Hypotheses	r19.29a.1	|- ( ( ( ph /\ x e. A ) /\ ps ) -> ch )
	r19.29a.2	|- ( ph -> E. x e. A ps )
Assertion	r19.29a	|- ( ph -> ch )

Proof

Step	Hyp	Ref	Expression
1		r19.29a.1	|- ( ( ( ph /\ x e. A ) /\ ps ) -> ch )
2		r19.29a.2	|- ( ph -> E. x e. A ps )
3	1	rexlimdva2	|- ( ph -> ( E. x e. A ps -> ch ) )
4	2 3	mpd	|- ( ph -> ch )