Theorem bj-trst 14031

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 831	. 2 ⊢ (STAB 𝜑 ↔ (¬ ¬ 𝜑 → 𝜑))
3	1, 2	sylibr 134	1 ⊢ (𝜑 → STAB 𝜑)

Syntax hints:  ¬ wn 3   → wi 4  STAB wstab 830

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108

This theorem depends on definitions:  df-bi 117  df-stab 831

This theorem is referenced by:  bj-sttru  14032  bj-nnst  14035  bj-nnbist  14036  bj-dcstab  14048