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Theorem exalim 1502
Description: One direction of a classical definition of existential quantification. One direction of Definition of [Margaris] p. 49. For a decidable proposition, this is an equivalence, as seen as dfexdc 1501. (Contributed by Jim Kingdon, 29-Jul-2018.)
Assertion
Ref Expression
exalim  |-  ( E. x ph  ->  -.  A. x  -.  ph )

Proof of Theorem exalim
StepHypRef Expression
1 alnex 1499 . . 3  |-  ( A. x  -.  ph  <->  -.  E. x ph )
21biimpi 120 . 2  |-  ( A. x  -.  ph  ->  -.  E. x ph )
32con2i 627 1  |-  ( E. x ph  ->  -.  A. x  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1351   E.wex 1492
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-5 1447  ax-gen 1449  ax-ie2 1494
This theorem depends on definitions:  df-bi 117  df-tru 1356  df-fal 1359
This theorem is referenced by:  n0rf  3435  ax9vsep  4123
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