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Theorem bddc 12953
Description: Decidability of a bounded formula is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdstab.1 BOUNDED 𝜑
Assertion
Ref Expression
bddc BOUNDED DECID 𝜑

Proof of Theorem bddc
StepHypRef Expression
1 bdstab.1 . . 3 BOUNDED 𝜑
21ax-bdn 12942 . . 3 BOUNDED ¬ 𝜑
31, 2ax-bdor 12941 . 2 BOUNDED (𝜑 ∨ ¬ 𝜑)
4 df-dc 805 . 2 (DECID 𝜑 ↔ (𝜑 ∨ ¬ 𝜑))
53, 4bd0r 12950 1 BOUNDED DECID 𝜑
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wo 682  DECID wdc 804  BOUNDED wbd 12937
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-bd0 12938  ax-bdor 12941  ax-bdn 12942
This theorem depends on definitions:  df-bi 116  df-dc 805
This theorem is referenced by: (None)
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