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Theorem bdstab 9282
Description: Stability of a bounded formula is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdstab.1 BOUNDED φ
Assertion
Ref Expression
bdstab BOUNDED STAB φ

Proof of Theorem bdstab
StepHypRef Expression
1 bdstab.1 . . . . 5 BOUNDED φ
21ax-bdn 9272 . . . 4 BOUNDED ¬ φ
32ax-bdn 9272 . . 3 BOUNDED ¬ ¬ φ
43, 1ax-bdim 9269 . 2 BOUNDED (¬ ¬ φφ)
5 df-stab 739 . 2 (STAB φ ↔ (¬ ¬ φφ))
64, 5bd0r 9280 1 BOUNDED STAB φ
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  STAB wstab 738  BOUNDED wbd 9267
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 9268  ax-bdim 9269  ax-bdn 9272
This theorem depends on definitions:  df-bi 110  df-stab 739
This theorem is referenced by: (None)
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