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Theorem pm10.251 27555
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 1530 . 2  |-  ( A. x  -.  ph  <->  -.  E. x ph )
2 19.2 1671 . . 3  |-  ( A. x ph  ->  E. x ph )
32con3i 127 . 2  |-  ( -. 
E. x ph  ->  -. 
A. x ph )
41, 3sylbi 187 1  |-  ( A. x  -.  ph  ->  -.  A. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1527   E.wex 1528
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-fal 1311  df-ex 1529
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