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Theorem bj-dcstab 13130
Description: A decidable formula is stable. (Contributed by BJ, 24-Nov-2023.) (Proof modification is discouraged.)
Assertion
Ref Expression
bj-dcstab (DECID 𝜑STAB 𝜑)

Proof of Theorem bj-dcstab
StepHypRef Expression
1 df-dc 821 . 2 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
2 bj-trst 13120 . . 3 (𝜑STAB 𝜑)
3 bj-fast 13121 . . 3 𝜑STAB 𝜑)
42, 3jaoi 706 . 2 ((𝜑 ∨ ¬ 𝜑) → STAB 𝜑)
51, 4sylbi 120 1 (DECID 𝜑STAB 𝜑)
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  wo 698  STAB wstab 816  DECID wdc 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  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116  df-stab 817  df-dc 821
This theorem is referenced by:  bj-nnbidc  13131
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