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Theorem nndc 836
Description: Double negation of decidability of a formula. Intuitionistic logic refutes undecidability (but does not prove decidability) of any formula. (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
nndc ¬ ¬ DECID 𝜑

Proof of Theorem nndc
StepHypRef Expression
1 nnexmid 835 . 2 ¬ ¬ (𝜑 ∨ ¬ 𝜑)
2 df-dc 820 . . 3 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
32notbii 657 . 2 DECID 𝜑 ↔ ¬ (𝜑 ∨ ¬ 𝜑))
41, 3mtbir 660 1 ¬ ¬ DECID 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wo 697  DECID wdc 819
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 603  ax-in2 604  ax-io 698
This theorem depends on definitions:  df-bi 116  df-dc 820
This theorem is referenced by:  bj-nnst  13017  bj-dcdc  13018  bj-stdc  13019
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