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Theorem bj-trst 13004
Description: A provable formula is stable. (Contributed by BJ, 24-Nov-2023.)
Assertion
Ref Expression
bj-trst (𝜑STAB 𝜑)

Proof of Theorem bj-trst
StepHypRef Expression
1 ax-1 6 . 2 (𝜑 → (¬ ¬ 𝜑𝜑))
2 df-stab 816 . 2 (STAB 𝜑 ↔ (¬ ¬ 𝜑𝜑))
31, 2sylibr 133 1 (𝜑STAB 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  STAB wstab 815
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 816
This theorem is referenced by:  bj-nnbist  13006  bj-dcstab  13014
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