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Theorem exnalim 1519
 Description: One direction of Theorem 19.14 of [Margaris] p. 90. In classical logic the converse also holds. (Contributed by Jim Kingdon, 15-Jul-2018.)
Assertion
Ref Expression
exnalim (x ¬ φ → ¬ xφ)

Proof of Theorem exnalim
StepHypRef Expression
1 alexim 1518 . 2 (xφ → ¬ x ¬ φ)
21con2i 545 1 (x ¬ φ → ¬ xφ)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4  ∀wal 1226  ∃wex 1362 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 532  ax-in2 533  ax-5 1316  ax-gen 1318  ax-ie1 1363  ax-ie2 1364  ax-4 1381  ax-17 1400  ax-ial 1409 This theorem depends on definitions:  df-bi 110  df-tru 1231  df-fal 1234  df-nf 1330 This theorem is referenced by:  exanaliim  1520  alexnim  1521  dtru  4222  brprcneu  5096
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