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

Theorem bj-fadc 13129
Description: A refutable formula is decidable. (Contributed by BJ, 24-Nov-2023.)
Assertion
Ref Expression
bj-fadc 𝜑DECID 𝜑)

Proof of Theorem bj-fadc
StepHypRef Expression
1 olc 701 . 2 𝜑 → (𝜑 ∨ ¬ 𝜑))
2 df-dc 821 . 2 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
31, 2sylibr 133 1 𝜑DECID 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 698  DECID wdc 820
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 699
This theorem depends on definitions:  df-bi 116  df-dc 821
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator