Theorem bj-trst 13620

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

Assertion

Ref	Expression
bj-trst	⊢ (𝜑 → STAB 𝜑)

Proof of Theorem bj-trst

Step	Hyp	Ref	Expression
1		ax-1 6	. 2 ⊢ (𝜑 → (¬ ¬ 𝜑 → 𝜑))
2		df-stab 821	. 2 ⊢ (STAB 𝜑 ↔ (¬ ¬ 𝜑 → 𝜑))
3	1, 2	sylibr 133	1 ⊢ (𝜑 → STAB 𝜑)

Syntax hints:  ¬ wn 3   → wi 4  STAB wstab 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

This theorem depends on definitions:  df-bi 116  df-stab 821

This theorem is referenced by:  bj-sttru  13621  bj-nnst  13624  bj-nnbist  13625  bj-dcstab  13637