Theorem r19.29an

Description: A commonly used pattern in the spirit of r19.29 . (Contributed by Thierry Arnoux, 29-Dec-2019) (Proof shortened by Wolf Lammen, 17-Jun-2023)

	Ref	Expression
Hypothesis	rexlimdva2.1	|- ( ( ( ph /\ x e. A ) /\ ps ) -> ch )
Assertion	r19.29an	|- ( ( ph /\ E. x e. A ps ) -> ch )

Proof

Step	Hyp	Ref	Expression
1		rexlimdva2.1	|- ( ( ( ph /\ x e. A ) /\ ps ) -> ch )
2	1	rexlimdva2	|- ( ph -> ( E. x e. A ps -> ch ) )
3	2	imp	|- ( ( ph /\ E. x e. A ps ) -> ch )