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Theorem spsd 1767
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 1759 . 2  |-  ( A. x ps  ->  ps )
2 spsd.1 . 2  |-  ( ph  ->  ( ps  ->  ch ) )
31, 2syl5 30 1  |-  ( ph  ->  ( A. x ps 
->  ch ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1546
This theorem is referenced by:  ax10lem2  1989  ax10lem4OLD  1996  moexex  2323  zorn2lem4  8335  zorn2lem5  8336  axpowndlem3  8430  axacndlem5  8442  ax4567  27469  cbv3hvNEW7  29152  ax10lem4NEW7  29177  ax7w2AUX7  29350  ax7w7tAUX7  29356
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-11 1757
This theorem depends on definitions:  df-bi 178  df-ex 1548
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