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Theorem pm10.53 36579
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 pm2.21 112 . 2  |-  ( -. 
E. x ph  ->  ( E. x ph  ->  A. x ps ) )
2 19.38 1708 . 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 setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1436   E.wex 1660
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1666  ax-4 1679
This theorem depends on definitions:  df-bi 189  df-ex 1661
This theorem is referenced by: (None)
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