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Theorem spsd 1740
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 1716 . 2  |-  ( A. x ps  ->  ps )
2 spsd.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2syl5 28 1  |-  ( ph  ->  ( A. x ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1527
This theorem is referenced by:  ax10lem4  1881  moexex  2212  zorn2lem4  8126  zorn2lem5  8127  axpowndlem3  8221  axacndlem5  8233  ax4567  27601
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-11 1715
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