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

Theorem alinexa 1491
Description: A transformation of quantifiers and logical connectives. (Contributed by NM, 19-Aug-1993.)
Assertion
Ref Expression
alinexa (x(φ → ¬ ψ) ↔ ¬ x(φ ψ))

Proof of Theorem alinexa
StepHypRef Expression
1 imnan 623 . . 3 ((φ → ¬ ψ) ↔ ¬ (φ ψ))
21albii 1356 . 2 (x(φ → ¬ ψ) ↔ x ¬ (φ ψ))
3 alnex 1385 . 2 (x ¬ (φ ψ) ↔ ¬ x(φ ψ))
42, 3bitri 173 1 (x(φ → ¬ ψ) ↔ ¬ x(φ ψ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97  wb 98  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:  sbnv  1765  ralnex  2310
  Copyright terms: Public domain W3C validator