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Theorem pm10.53 27664
Description: Theorem *10.53 in [WhiteheadRussell] p. 155. (Contributed by Andrew Salmon, 24-May-2011.)
Assertion
Ref Expression
pm10.53  |-  ( -. 
E. x ph  ->  A. x ( ph  ->  ps ) )

Proof of Theorem pm10.53
StepHypRef Expression
1 pm2.21 100 . 2  |-  ( -. 
E. x ph  ->  ( E. x ph  ->  A. x ps ) )
2 19.38 1822 . 2  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( ph  ->  ps ) )
31, 2syl 15 1  |-  ( -. 
E. x ph  ->  A. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1530   E.wex 1531
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535
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