Theorem rexlimdv

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by NM, 14-Nov-2002) (Proof shortened by Eric Schmidt, 22-Dec-2006) Reduce dependencies on axioms. (Revised by Wolf Lammen, 14-Jan-2020)

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

Proof

Step	Hyp	Ref	Expression
1		rexlimdv.1	|- ( ph -> ( x e. A -> ( ps -> ch ) ) )
2	1	com3l	|- ( x e. A -> ( ps -> ( ph -> ch ) ) )
3	2	rexlimiv	|- ( E. x e. A ps -> ( ph -> ch ) )
4	3	com12	|- ( ph -> ( E. x e. A ps -> ch ) )