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Theorem hbim1 1732
Description: A closed form of hbim 1725. (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 12 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  A. x ps ) )
3 hbim1.1 . . 3  |-  ( ph  ->  A. x ph )
4319.21h 1731 . 2  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )
52, 4sylibr 203 1  |-  ( (
ph  ->  ps )  ->  A. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem is referenced by:  ax12olem6  1873  ax15  1961  a12study2  29134
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-11 1715
This theorem depends on definitions:  df-bi 177
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