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Theorem ralimiaa 2559
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 115 . 2  |-  ( x  e.  A  ->  ( ph  ->  ps ) )
32ralimia 2558 1  |-  ( A. x  e.  A  ph  ->  A. x  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 104    e. wcel 2167   A.wral 2475
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1461  ax-gen 1463
This theorem depends on definitions:  df-bi 117  df-ral 2480
This theorem is referenced by:  ralrnmpt  5704  rexrnmpt  5705  acexmidlem2  5919  mptelixpg  6793  trirec0  15688
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