ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  nnexmid GIF version

Theorem nnexmid 845
Description: Double negation of decidability of a formula. See also comment of nndc 846 to avoid a pitfall that could come from the label "nnexmid". This theorem can also be proved from bj-nnor 13690 as in bj-nndcALT 13714. (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
nnexmid ¬ ¬ (𝜑 ∨ ¬ 𝜑)

Proof of Theorem nnexmid
StepHypRef Expression
1 pm3.24 688 . 2 ¬ (¬ 𝜑 ∧ ¬ ¬ 𝜑)
2 ioran 747 . 2 (¬ (𝜑 ∨ ¬ 𝜑) ↔ (¬ 𝜑 ∧ ¬ ¬ 𝜑))
31, 2mtbir 666 1 ¬ ¬ (𝜑 ∨ ¬ 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wa 103  wo 703
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 609  ax-in2 610  ax-io 704
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  nndc  846  exmid1stab  13955
  Copyright terms: Public domain W3C validator