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Theorem pm10.53 26727
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 1791 . 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 1532   E.wex 1537
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-4 1692
This theorem depends on definitions:  df-bi 179  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540
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