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Theorem pm3.24 852
Description: Law of noncontradiction. Theorem *3.24 of [WhiteheadRussell] p. 111 (who call it the "law of contradiction"). (Contributed by NM, 16-Sep-1993.) (Proof shortened by Wolf Lammen, 24-Nov-2012.)
Assertion
Ref Expression
pm3.24 ¬ (φ ¬ φ)

Proof of Theorem pm3.24
StepHypRef Expression
1 id 19 . 2 (φφ)
2 iman 413 . 2 ((φφ) ↔ ¬ (φ ¬ φ))
31, 2mpbi 199 1 ¬ (φ ¬ φ)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4   wa 358
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-an 360
This theorem is referenced by:  pm4.43  893  nonconne  2523  pssirr  3369  indifdir  3511  dfnul2  3552  dfnul3  3553  rabnc  3574  nincompl  4072  imadif  5171
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