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Theorem pm10.251 26908
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 1569 . 2  |-  ( A. x  -.  ph  <->  -.  E. x ph )
2 19.2 1759 . . 3  |-  ( A. x ph  ->  E. x ph )
32con3i 129 . 2  |-  ( -. 
E. x ph  ->  -. 
A. x ph )
41, 3sylbi 189 1  |-  ( A. x  -.  ph  ->  -.  A. x ph )
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-4 1692
This theorem depends on definitions:  df-bi 179  df-ex 1538
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