Theorem bj-fadc 16782

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

Assertion

Ref	Expression
bj-fadc	⊢ (¬ 𝜑 → DECID 𝜑)

Proof of Theorem bj-fadc

Step	Hyp	Ref	Expression
1		olc 723	. 2 ⊢ (¬ 𝜑 → (𝜑 ∨ ¬ 𝜑))
2		df-dc 847	. 2 ⊢ (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
3	1, 2	sylibr 134	1 ⊢ (¬ 𝜑 → DECID 𝜑)

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 720  DECID wdc 846

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This proof depends on definitions:  df-bi 117  df-dc 847

This theorem is used by:  bj-dcfal  16783