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Theorem bddc 9263
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 9252 . . 3 BOUNDED ¬ φ
31, 2ax-bdor 9251 . 2 BOUNDED (φ ¬ φ)
4 df-dc 742 . 2 (DECID φ ↔ (φ ¬ φ))
53, 4bd0r 9260 1 BOUNDED DECID φ
Colors of variables: wff set class
Syntax hints:  ¬ wn 3   wo 628  DECID wdc 741  BOUNDED wbd 9247
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-bd0 9248  ax-bdor 9251  ax-bdn 9252
This theorem depends on definitions:  df-bi 110  df-dc 742
This theorem is referenced by: (None)
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