Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bj-trdc GIF version

Theorem bj-trdc 14160
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 712 . 2 (𝜑 → (𝜑 ∨ ¬ 𝜑))
2 df-dc 835 . 2 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
31, 2sylibr 134 1 (𝜑DECID 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 708  DECID wdc 834
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 709
This theorem depends on definitions:  df-bi 117  df-dc 835
This theorem is referenced by:  bj-dctru  14161  bj-nnbidc  14165
  Copyright terms: Public domain W3C validator