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Theorem pm10.251 38559
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 1706 . 2 |- ( A. x -. ph <-> -. E. x ph )
2 19.2 1892 . . 3 |- ( A. x ph -> E. x ph )
32con3i 150 . 2 |- ( -. E. x ph -> -. A. x ph )
41, 3sylbi 207 1 |- ( A. x -. ph -> -. A. x ph )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3   -> wi 4   A.wal 1481   E.wex 1704
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1722  ax-4 1737  ax-6 1888
This theorem depends on definitions:  df-bi 197  df-ex 1705
This theorem is referenced by: (None)
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