NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  pm4.52 GIF version

Theorem pm4.52 477
Description: Theorem *4.52 of [WhiteheadRussell] p. 120. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Nov-2012.)
Assertion
Ref Expression
pm4.52 ((φ ¬ ψ) ↔ ¬ (¬ φ ψ))

Proof of Theorem pm4.52
StepHypRef Expression
1 annim 414 . 2 ((φ ¬ ψ) ↔ ¬ (φψ))
2 imor 401 . 2 ((φψ) ↔ (¬ φ ψ))
31, 2xchbinx 301 1 ((φ ¬ ψ) ↔ ¬ (¬ φ ψ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176   wo 357   wa 358
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360
This theorem is referenced by:  pm4.53  478
  Copyright terms: Public domain W3C validator