ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  pm2.01da GIF version

Theorem pm2.01da 575
Description: Deduction based on reductio ad absurdum. (Contributed by Mario Carneiro, 9-Feb-2017.)
Hypothesis
Ref Expression
pm2.01da.1 ((𝜑𝜓) → ¬ 𝜓)
Assertion
Ref Expression
pm2.01da (𝜑 → ¬ 𝜓)

Proof of Theorem pm2.01da
StepHypRef Expression
1 pm2.01da.1 . . 3 ((𝜑𝜓) → ¬ 𝜓)
21ex 112 . 2 (𝜑 → (𝜓 → ¬ 𝜓))
32pm2.01d 558 1 (𝜑 → ¬ 𝜓)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 101
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 105  ax-in1 554
This theorem is referenced by:  efrirr  4117
  Copyright terms: Public domain W3C validator