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Theorem ralimia 2468
Description: Inference quantifying both antecedent and consequent. (Contributed by NM, 19-Jul-1996.)
Hypothesis
Ref Expression
ralimia.1  |-  ( x  e.  A  ->  ( ph  ->  ps ) )
Assertion
Ref Expression
ralimia  |-  ( A. x  e.  A  ph  ->  A. x  e.  A  ps )

Proof of Theorem ralimia
StepHypRef Expression
1 ralimia.1 . . 3  |-  ( x  e.  A  ->  ( ph  ->  ps ) )
21a2i 11 . 2  |-  ( ( x  e.  A  ->  ph )  ->  ( x  e.  A  ->  ps ) )
32ralimi2 2467 1  |-  ( A. x  e.  A  ph  ->  A. x  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1463   A.wral 2391
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1406  ax-gen 1408
This theorem depends on definitions:  df-bi 116  df-ral 2396
This theorem is referenced by:  ralimiaa  2469  ralimi  2470  r19.12  2513  rr19.3v  2795  rr19.28v  2796  ffvresb  5549  f1mpt  5638  ixpf  6580  peano2nnnn  7625  peano5nnnn  7664  peano5nni  8680  peano2nn  8689  serf0  11061  baspartn  12112
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