Theorem ralimiaa 2425

Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 4-Aug-2007.)

Hypothesis

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

Assertion

Ref	Expression
ralimiaa	|- ( A. x e. A ph -> A. x e. A ps )

Proof of Theorem ralimiaa

Step	Hyp	Ref	Expression
1		ralimiaa.1	. . 3 |- ( ( x e. A /\ ph ) -> ps )
2	1	ex 113	. 2 |- ( x e. A -> ( ph -> ps ) )
3	2	ralimia 2424	1 |- ( A. x e. A ph -> A. x e. A ps )

Syntax hints:   -> wi 4   /\ wa 102   e. wcel 1433   A.wral 2348

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 1376  ax-gen 1378

This theorem depends on definitions:  df-bi 115  df-ral 2353

This theorem is referenced by:  ralrnmpt  5330  rexrnmpt  5331  acexmidlem2  5529