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Theorem pm2.01 590
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 825 which only holds for some propositions. Also called weak Clavius law. (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 588 1 ((𝜑 → ¬ 𝜑) → ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-in1 588
This theorem is referenced by:  pm2.01d  592  con2d  598  pm2.65i  613  pm4.8  681  notnotsnex  4081
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