Theorem rexlimdva2

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by Glauco Siliprandi, 2-Jan-2022)

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

Proof

Step	Hyp	Ref	Expression
1		rexlimdva2.1	|- ( ( ( ph /\ x e. A ) /\ ps ) -> ch )
2	1	exp31	|- ( ph -> ( x e. A -> ( ps -> ch ) ) )
3	2	rexlimdv	|- ( ph -> ( E. x e. A ps -> ch ) )