Theorem bj-trdc 15189

Description: A provable formula is decidable. (Contributed by BJ, 24-Nov-2023.)

Assertion

Ref	Expression
bj-trdc	⊢ (𝜑 → DECID 𝜑)

Proof of Theorem bj-trdc

Step	Hyp	Ref	Expression
1		orc 713	. 2 ⊢ (𝜑 → (𝜑 ∨ ¬ 𝜑))
2		df-dc 836	. 2 ⊢ (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
3	1, 2	sylibr 134	1 ⊢ (𝜑 → DECID 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 709  DECID wdc 835

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 710

This theorem depends on definitions:  df-bi 117  df-dc 836

This theorem is referenced by:  bj-dctru  15190  bj-nnbidc  15194