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Theorem ralimia 2436
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 2435 1  |-  ( A. x  e.  A  ph  ->  A. x  e.  A  ps )
Colors of variables: wff set class
Syntax hints:    -> wi 4    e. wcel 1438   A.wral 2359
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 1381  ax-gen 1383
This theorem depends on definitions:  df-bi 115  df-ral 2364
This theorem is referenced by:  ralimiaa  2437  ralimi  2438  r19.12  2478  rr19.3v  2755  rr19.28v  2756  ffvresb  5461  f1mpt  5550  peano2nnnn  7390  peano5nnnn  7427  peano5nni  8425  peano2nn  8434  serf0  10741
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