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Theorem pm10.251 29759
Description: Theorem *10.251 in [WhiteheadRussell] p. 149. (Contributed by Andrew Salmon, 17-Jun-2011.)
Assertion
Ref Expression
pm10.251  |-  ( A. x  -.  ph  ->  -.  A. x ph )

Proof of Theorem pm10.251
StepHypRef Expression
1 alnex 1589 . 2  |-  ( A. x  -.  ph  <->  -.  E. x ph )
2 19.2 1714 . . 3  |-  ( A. x ph  ->  E. x ph )
32con3i 135 . 2  |-  ( -. 
E. x ph  ->  -. 
A. x ph )
41, 3sylbi 195 1  |-  ( A. x  -.  ph  ->  -.  A. x ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1368   E.wex 1587
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1592  ax-4 1603  ax-6 1710
This theorem depends on definitions:  df-bi 185  df-ex 1588
This theorem is referenced by: (None)
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