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Theorem exalim 1388
 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 1387. (Contributed by Jim Kingdon, 29-Jul-2018.)
Assertion
Ref Expression
exalim (xφ → ¬ x ¬ φ)

Proof of Theorem exalim
StepHypRef Expression
1 alnex 1385 . . 3 (x ¬ φ ↔ ¬ xφ)
21biimpi 113 . 2 (x ¬ φ → ¬ xφ)
32con2i 557 1 (xφ → ¬ x ¬ φ)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1240  ∃wex 1378 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-5 1333  ax-gen 1335  ax-ie2 1380 This theorem depends on definitions:  df-bi 110  df-tru 1245  df-fal 1248 This theorem is referenced by:  n0rf  3227  ax9vsep  3871
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