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Theorem ralimiaa 2400
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
StepHypRef Expression
1 ralimiaa.1 . . 3  |-  ( ( x  e.  A  /\  ph )  ->  ps )
21ex 112 . 2  |-  ( x  e.  A  ->  ( ph  ->  ps ) )
32ralimia 2399 1  |-  ( A. x  e.  A  ph  ->  A. x  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 101    e. wcel 1409   A.wral 2323
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-gen 1354
This theorem depends on definitions:  df-bi 114  df-ral 2328
This theorem is referenced by:  ralrnmpt  5337  rexrnmpt  5338  acexmidlem2  5537
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