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Theorem bj-trdc 12959
Description: A provable formula is decidable. (Contributed by BJ, 24-Nov-2023.)
Assertion
Ref Expression
bj-trdc (𝜑DECID 𝜑)

Proof of Theorem bj-trdc
StepHypRef Expression
1 orc 701 . 2 (𝜑 → (𝜑 ∨ ¬ 𝜑))
2 df-dc 820 . 2 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
31, 2sylibr 133 1 (𝜑DECID 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  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-io 698
This theorem depends on definitions:  df-bi 116  df-dc 820
This theorem is referenced by:  bj-nnbidc  12962
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