ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.65da GIF version

Theorem pm2.65da 586
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 108 . 2 (φ → (ψχ))
3 pm2.65da.2 . . 3 ((φ ψ) → ¬ χ)
43ex 108 . 2 (φ → (ψ → ¬ χ))
52, 4pm2.65d 585 1 (φ → ¬ ψ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem is referenced by:  condandc  774  nelrdva  2740  prodgt0  7599  ixxdisj  8542  icodisj  8630
  Copyright terms: Public domain W3C validator