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Theorem spsd 1761
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 1753 . 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 1545
This theorem is referenced by:  ax10lem4  1954  moexex  2286  zorn2lem4  8273  zorn2lem5  8274  axpowndlem3  8368  axacndlem5  8380  ax4567  27107  ax10lem4NEW7  28896
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1551  ax-5 1562  ax-17 1621  ax-9 1659  ax-8 1680  ax-11 1751
This theorem depends on definitions:  df-bi 177  df-ex 1547
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