Theorem bj-trdc 13787

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 707	. 2 ⊢ (𝜑 → (𝜑 ∨ ¬ 𝜑))
2		df-dc 830	. 2 ⊢ (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
3	1, 2	sylibr 133	1 ⊢ (𝜑 → DECID 𝜑)

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 703  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-io 704

This theorem depends on definitions:  df-bi 116  df-dc 830

This theorem is referenced by:  bj-dctru  13788  bj-nnbidc  13792