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Mirrors > Home > ILE Home > Th. List > pm2.01 | GIF version |
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 841 which only holds for some propositions. Also called weak Clavius law. (Contributed by Mario Carneiro, 12-May-2015.) |
Ref | Expression |
---|---|
pm2.01 | ⊢ ((𝜑 → ¬ 𝜑) → ¬ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-in1 604 | 1 ⊢ ((𝜑 → ¬ 𝜑) → ¬ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 → wi 4 |
This theorem was proved from axioms: ax-in1 604 |
This theorem is referenced by: pm2.01d 608 con2d 614 pm2.65i 629 pm4.8 697 notnotsnex 4148 |
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