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Theorem bj-dcdc 13759
Description: Decidability of a proposition is decidable if and only if that proposition is decidable. DECID is idempotent. (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
bj-dcdc (DECID DECID 𝜑DECID 𝜑)

Proof of Theorem bj-dcdc
StepHypRef Expression
1 nndc 846 . 2 ¬ ¬ DECID 𝜑
2 bj-nnbidc 13757 . 2 (¬ ¬ DECID 𝜑 → (DECID DECID 𝜑DECID 𝜑))
31, 2ax-mp 5 1 (DECID DECID 𝜑DECID 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 104  DECID wdc 829
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  df-stab 826  df-dc 830
This theorem is referenced by: (None)
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