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Theorem pm10.53 26961
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 pm2.21 102 . 2  |-  ( -. 
E. x ph  ->  ( E. x ph  ->  A. x ps ) )
2 19.38 1812 . 2  |-  ( ( E. x ph  ->  A. x ps )  ->  A. x ( ph  ->  ps ) )
31, 2syl 17 1  |-  ( -. 
E. x ph  ->  A. x ( ph  ->  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6   A.wal 1528   E.wex 1529
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-gen 1534  ax-5 1545  ax-17 1604  ax-9 1637  ax-8 1645  ax-6 1704  ax-11 1716
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1312  df-ex 1530  df-nf 1533
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