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

Theorem pm2.01 579
Description: Reductio ad absurdum. Theorem *2.01 of [WhiteheadRussell] p. 100. This is valid intuitionistically (in the terminology of Section 1.2 of [Bauer] p. 482 it is a proof of negation not a proof by contradiction); compare with pm2.18dc 784 which only holds for some propositions. (Contributed by Mario Carneiro, 12-May-2015.)
Assertion
Ref Expression
pm2.01 ((𝜑 → ¬ 𝜑) → ¬ 𝜑)

Proof of Theorem pm2.01
StepHypRef Expression
1 ax-in1 577 1 ((𝜑 → ¬ 𝜑) → ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-in1 577
This theorem is referenced by:  pm2.01d  581  con2d  587  pm2.65i  601  pm4.8  656
  Copyright terms: Public domain W3C validator