Theorem rexlimdv3a 2480

Description: Inference from Theorem 19.23 of [Margaris] p. 90 (restricted quantifier version). Frequently-used variant of rexlimdv 2477. (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 1138	. 2 |- ( ph -> ( x e. A -> ( ps -> ch ) ) )
3	2	rexlimdv 2477	1 |- ( ph -> ( E. x e. A ps -> ch ) )

Syntax hints:   -> wi 4   /\ w3a 920   e. wcel 1434   E.wrex 2350

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-4 1441  ax-17 1460  ax-ial 1468  ax-i5r 1469

This theorem depends on definitions:  df-bi 115  df-3an 922  df-nf 1391  df-ral 2354  df-rex 2355

This theorem is referenced by:  resqrtcl  10053