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Theorem pm3.24 614
 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 notnot1 547 . 2 (φ → ¬ ¬ φ)
2 imnan 611 . 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 532  ax-in2 533 This theorem depends on definitions:  df-bi 110 This theorem is referenced by:  pm4.43  842  excxor  1252  nonconne  2192  pssirr  3017  sspssn  3021  dfnul2  3199  dfnul3  3200  rabnc  3223  axnul  3852  nnexmid  7145
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