ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  exanaliim Structured version   GIF version

Theorem exanaliim 1522
Description: A transformation of quantifiers and logical connectives. In classical logic the converse also holds. (Contributed by Jim Kingdon, 15-Jul-2018.)
Assertion
Ref Expression
exanaliim (x(φ ¬ ψ) → ¬ x(φψ))

Proof of Theorem exanaliim
StepHypRef Expression
1 annimim 775 . . 3 ((φ ¬ ψ) → ¬ (φψ))
21eximi 1475 . 2 (x(φ ¬ ψ) → x ¬ (φψ))
3 exnalim 1521 . 2 (x ¬ (φψ) → ¬ x(φψ))
42, 3syl 14 1 (x(φ ¬ ψ) → ¬ x(φψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97  wal 1226  wex 1363
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 1364  ax-ie2 1365  ax-4 1382  ax-17 1401  ax-ial 1410
This theorem depends on definitions:  df-bi 110  df-tru 1231  df-fal 1234  df-nf 1330
This theorem is referenced by:  rexnalim  2294  nssr  2979  nssssr  3931  brprcneu  5094
  Copyright terms: Public domain W3C validator