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Theorem pm2.01 180
Description: Reductio ad absurdum. Theorem *2.01 of [WhiteheadRussell] p. 100. Also called the weak Clavius law, and provable in minimal calculus, contrary to the Clavius law pm2.18 122. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Mel L. O'Cat, 21-Nov-2008.) (Proof shortened by Wolf Lammen, 31-Oct-2012.)
Assertion
Ref Expression
pm2.01 ((𝜑 → ¬ 𝜑) → ¬ 𝜑)

Proof of Theorem pm2.01
StepHypRef Expression
1 id 22 . 2 𝜑 → ¬ 𝜑)
21, 1ja 173 1 ((𝜑 → ¬ 𝜑) → ¬ 𝜑)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem is referenced by:  bijust  195  pm4.8  380  axin1  2594  dtrucor2  4867  ominf  8117  elirr  8450  hfninf  31927  bj-pm2.01i  32184  bj-nimn  32185  bj-dtrucor2v  32436
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