Theorem rexlimdvaa 2740

Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). (Contributed by Mario Carneiro, 15-Jun-2016.)

Hypothesis

Ref	Expression
rexlimdvaa.1	|- ((ph /\ (x e. A /\ ps)) -> ch)

Assertion

Ref	Expression
rexlimdvaa	|- (ph -> (E.x e. A ps -> ch))

Distinct variable groups:   ph,x   ch,x

Allowed substitution hints:   ps(x)   A(x)

Proof of Theorem rexlimdvaa

Step	Hyp	Ref	Expression
1		rexlimdvaa.1	. . 3 |- ((ph /\ (x e. A /\ ps)) -> ch)
2	1	expr 598	. 2 |- ((ph /\ x e. A) -> (ps -> ch))
3	2	rexlimdva 2739	1 |- (ph -> (E.x e. A ps -> ch))

Syntax hints:   -> wi 4   /\ wa 358   e. wcel 1710  E.wrex 2616

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-ral 2620  df-rex 2621

This theorem is referenced by:  rexlimddv  2743