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Theorem hbim1 1973
Description: A closed form of hbim 1977. (Contributed by NM, 2-Jun-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 14 . 2  |-  ( (
ph  ->  ps )  -> 
( ph  ->  A. x ps ) )
3 hbim1.1 . . 3  |-  ( ph  ->  A. x ph )
4319.21h 1961 . 2  |-  ( A. x ( ph  ->  ps )  <->  ( ph  ->  A. x ps ) )
52, 4sylibr 215 1  |-  ( (
ph  ->  ps )  ->  A. x ( ph  ->  ps ) )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4   A.wal 1435
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-10 1886  ax-12 1904
This theorem depends on definitions:  df-bi 188  df-ex 1660  df-nf 1664
This theorem is referenced by:  nfim1  1974  hbim  1977  axc14  2164
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