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Theorem spsd 1917
Description: Deduction generalizing antecedent. (Contributed by NM, 17-Aug-1994.)
Hypothesis
Ref Expression
spsd.1  |-  ( ph  ->  ( ps  ->  ch ) )
Assertion
Ref Expression
spsd  |-  ( ph  ->  ( A. x ps 
->  ch ) )

Proof of Theorem spsd
StepHypRef Expression
1 sp 1909 . 2  |-  ( A. x ps  ->  ps )
2 spsd.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2syl5 33 1  |-  ( ph  ->  ( A. x ps 
->  ch ) )
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-12 1904
This theorem depends on definitions:  df-bi 188  df-ex 1660
This theorem is referenced by:  axc11nlem  1993  axc11nlemOLD  2101  equveli  2141  nfsb4t  2181  mo2v  2270  mo2vOLD  2271  moexex  2335  2eu6  2354  zorn2lem4  8918  zorn2lem5  8919  axpowndlem3  9013  axacndlem5  9025  bj-axc11nlemv  31136  wl-equsal1i  31624  axc5c4c711  36437
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