Theorem rexlimdv3a 2741

Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). Frequently-used variant of rexlimdv 2738. (Contributed by NM, 7-Jun-2015.)

Hypothesis

Ref	Expression
rexlimdv3a.1	|- ((ph /\ x e. A /\ ps) -> ch)

Assertion

Ref	Expression
rexlimdv3a	|- (ph -> (E.x e. A ps -> ch))

Distinct variable groups:   ph,x   ch,x

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

Proof of Theorem rexlimdv3a

Step	Hyp	Ref	Expression
1		rexlimdv3a.1	. . 3 |- ((ph /\ x e. A /\ ps) -> ch)
2	1	3exp 1150	. 2 |- (ph -> (x e. A -> (ps -> ch)))
3	2	rexlimdv 2738	1 |- (ph -> (E.x e. A ps -> ch))

Syntax hints:   -> wi 4   /\ w3a 934   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-3an 936  df-ex 1542  df-nf 1545  df-ral 2620  df-rex 2621

This theorem is referenced by: (None)