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Theorem spsd 1956
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 1948 . 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 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-12 1944
This theorem depends on definitions:  df-bi 190  df-an 377  df-ex 1675
This theorem is referenced by:  axc11nlem  2032  axc11nlemALT  2153  equveli  2191  nfsb4t  2229  mo2v  2317  moexex  2381  2eu6  2398  zorn2lem4  8960  zorn2lem5  8961  axpowndlem3  9055  axacndlem5  9067  bj-axc11nlemv  31393  wl-equsal1i  31922  axc5c4c711  36797
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