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Theorem bj-stst 13745
Description: Stability of a proposition is stable if and only if that proposition is stable. STAB is idempotent. (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
bj-stst (STAB STAB 𝜑STAB 𝜑)

Proof of Theorem bj-stst
StepHypRef Expression
1 bj-nnst 13743 . 2 ¬ ¬ STAB 𝜑
2 bj-nnbist 13744 . 2 (¬ ¬ STAB 𝜑 → (STAB STAB 𝜑STAB 𝜑))
31, 2ax-mp 5 1 (STAB STAB 𝜑STAB 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wb 104  STAB wstab 825
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 609  ax-in2 610
This theorem depends on definitions:  df-bi 116  df-stab 826
This theorem is referenced by: (None)
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