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Theorem pm10.251 27513
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 1552 . 2  |-  ( A. x  -.  ph  <->  -.  E. x ph )
2 19.2 1671 . . 3  |-  ( A. x ph  ->  E. x ph )
32con3i 129 . 2  |-  ( -. 
E. x ph  ->  -. 
A. x ph )
41, 3sylbi 188 1  |-  ( A. x  -.  ph  ->  -.  A. x ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1549   E.wex 1550
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-9 1666
This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551
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