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Theorem nnexmid 9873
Description: Double negation of excluded middle. Intuitionistic logic refutes the negation of excluded middle (but, of course, does not prove excluded middle) for any formula. (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
nnexmid ¬ ¬ (𝜑 ∨ ¬ 𝜑)

Proof of Theorem nnexmid
StepHypRef Expression
1 pm3.24 627 . 2 ¬ (¬ 𝜑 ∧ ¬ ¬ 𝜑)
2 ioran 669 . 2 (¬ (𝜑 ∨ ¬ 𝜑) ↔ (¬ 𝜑 ∧ ¬ ¬ 𝜑))
31, 2mtbir 596 1 ¬ ¬ (𝜑 ∨ ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 97  wo 629
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  ax-io 630
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  nndc  9874
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