NFE Home New Foundations Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  NFE Home  >  Th. List  >  pm2.65da GIF version

Theorem pm2.65da 559
Description: Deduction rule for proof by contradiction. (Contributed by NM, 12-Jun-2014.)
Hypotheses
Ref Expression
pm2.65da.1 ((φ ψ) → χ)
pm2.65da.2 ((φ ψ) → ¬ χ)
Assertion
Ref Expression
pm2.65da (φ → ¬ ψ)

Proof of Theorem pm2.65da
StepHypRef Expression
1 pm2.65da.1 . . 3 ((φ ψ) → χ)
21ex 423 . 2 (φ → (ψχ))
3 pm2.65da.2 . . 3 ((φ ψ) → ¬ χ)
43ex 423 . 2 (φ → (ψ → ¬ χ))
52, 4pm2.65d 166 1 (φ → ¬ ψ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   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:  condan  769
  Copyright terms: Public domain W3C validator