NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  pm4.15 GIF version

Theorem pm4.15 564
Description: Theorem *4.15 of [WhiteheadRussell] p. 117. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 18-Nov-2012.)
Assertion
Ref Expression
pm4.15 (((φ ψ) → ¬ χ) ↔ ((ψ χ) → ¬ φ))

Proof of Theorem pm4.15
StepHypRef Expression
1 con2b 324 . 2 (((ψ χ) → ¬ φ) ↔ (φ → ¬ (ψ χ)))
2 nan 563 . 2 ((φ → ¬ (ψ χ)) ↔ ((φ ψ) → ¬ χ))
31, 2bitr2i 241 1 (((φ ψ) → ¬ χ) ↔ ((ψ χ) → ¬ φ))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 176   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-an 360
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator