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Theorem hbim1 1830
Description: A closed form of hbim 1837. (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 13 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  A. x ps ) )
3 hbim1.1 . . 3  |-  ( ph  ->  A. x ph )
4319.21h 1816 . 2  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )
52, 4sylibr 205 1  |-  ( (
ph  ->  ps )  ->  A. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1550
This theorem is referenced by:  nfim1  1831  hbim  1837  ax12olem6OLD  2017  ax15  2109  ax12olem6NEW7  29533  ax15NEW7  29610
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-11 1762
This theorem depends on definitions:  df-bi 179  df-ex 1552  df-nf 1555
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