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Theorem pm3.24 683
 Description: Law of noncontradiction. Theorem *3.24 of [WhiteheadRussell] p. 111 (who call it the "law of contradiction"). (Contributed by NM, 16-Sep-1993.) (Revised by Mario Carneiro, 2-Feb-2015.)
Assertion
Ref Expression
pm3.24 ¬ (𝜑 ∧ ¬ 𝜑)

Proof of Theorem pm3.24
StepHypRef Expression
1 notnot 619 . 2 (𝜑 → ¬ ¬ 𝜑)
2 imnan 680 . 2 ((𝜑 → ¬ ¬ 𝜑) ↔ ¬ (𝜑 ∧ ¬ 𝜑))
31, 2mpbi 144 1 ¬ (𝜑 ∧ ¬ 𝜑)
 Colors of variables: wff set class Syntax hints:  ¬ wn 3   → wi 4   ∧ wa 103 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 604  ax-in2 605 This theorem depends on definitions:  df-bi 116 This theorem is referenced by:  nnexmid  836  pm4.43  934  excxor  1357  nonconne  2321  dfnul2  3369  dfnul3  3370  rabnc  3399  axnul  4060  fiintim  6824  zeoxor  11600  unennn  11944
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