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Theorem nnexmid 7145
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 pm3.24 614 . 2 ¬ (¬ φ ¬ ¬ φ)
2 ioran 656 . 2 (¬ (φ ¬ φ) ↔ (¬ φ ¬ ¬ φ))
31, 2mtbir 583 1 ¬ ¬ (φ ¬ φ)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   wa 97   wo 616
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  ax-io 617
This theorem depends on definitions:  df-bi 110
This theorem is referenced by:  nndc  7146
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