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Theorem exalim 1432
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 1431. (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 1429 . . 3  |-  ( A. x  -.  ph  <->  -.  E. x ph )
21biimpi 118 . 2  |-  ( A. x  -.  ph  ->  -.  E. x ph )
32con2i 590 1  |-  ( E. x ph  ->  -.  A. x  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   A.wal 1283   E.wex 1422
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-5 1377  ax-gen 1379  ax-ie2 1424
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291
This theorem is referenced by:  n0rf  3267  ax9vsep  3909
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