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Theorem bj-dcst 14483
Description: Stability of a proposition is decidable if and only if that proposition is stable. (Contributed by BJ, 24-Nov-2023.)
Assertion
Ref Expression
bj-dcst (DECID STAB 𝜑STAB 𝜑)

Proof of Theorem bj-dcst
StepHypRef Expression
1 bj-nnst 14465 . 2 ¬ ¬ STAB 𝜑
2 bj-nnbidc 14479 . 2 (¬ ¬ STAB 𝜑 → (DECID STAB 𝜑STAB 𝜑))
31, 2ax-mp 5 1 (DECID STAB 𝜑STAB 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 105  STAB wstab 830  DECID wdc 834
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709
This theorem depends on definitions:  df-bi 117  df-stab 831  df-dc 835
This theorem is referenced by: (None)
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