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Theorem pm3.24 627
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 559 . 2 (𝜑 → ¬ ¬ 𝜑)
2 imnan 624 . 2 ((𝜑 → ¬ ¬ 𝜑) ↔ ¬ (𝜑 ∧ ¬ 𝜑))
31, 2mpbi 133 1 ¬ (𝜑 ∧ ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wa 97
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  pm4.43  856  excxor  1269  nonconne  2217  pssirr  3044  sspssn  3048  dfnul2  3226  dfnul3  3227  rabnc  3250  axnul  3882  nnexmid  9873
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