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Theorem pm2.01 192
 Description: Weak Clavius law. If a formula implies its negation, then it is false. A form of "reductio ad absurdum", which can be used in proofs by contradiction. Theorem *2.01 of [WhiteheadRussell] p. 100. Provable in minimal calculus, contrary to the Clavius law pm2.18 128. (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 189 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:  bijust0  207  pm4.8  396  axin1  2781  dtrucor2  5246  ominf  8706  elirr  9037  hfninf  33654  bj-pm2.01i  33905  bj-nimn  33906  bj-dtrucor2v  34147  remul01  39359
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