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Theorem hbim1 1462
Description: A closed form of hbim 1437. (Contributed by NM, 5-Aug-1993.)
Hypotheses
Ref Expression
hbim1.1  |-  ( ph  ->  A. x ph )
hbim1.2  |-  ( ph  ->  ( ps  ->  A. x ps ) )
Assertion
Ref Expression
hbim1  |-  ( (
ph  ->  ps )  ->  A. x ( ph  ->  ps ) )

Proof of Theorem hbim1
StepHypRef Expression
1 hbim1.2 . . 3  |-  ( ph  ->  ( ps  ->  A. x ps ) )
21a2i 11 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  A. x ps ) )
3 hbim1.1 . . 3  |-  ( ph  ->  A. x ph )
4319.21h 1449 . 2  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )
52, 4sylibr 137 1  |-  ( (
ph  ->  ps )  ->  A. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1241
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-gen 1338  ax-4 1400  ax-ial 1427  ax-i5r 1428
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  nfim1  1463  sbco2d  1840  sbco2vd  1841
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