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Theorem bdstab 12952
Description: Stability of a bounded formula is bounded. (Contributed by BJ, 3-Oct-2019.)
Hypothesis
Ref Expression
bdstab.1  |- BOUNDED  ph
Assertion
Ref Expression
bdstab  |- BOUNDED STAB  ph

Proof of Theorem bdstab
StepHypRef Expression
1 bdstab.1 . . . . 5  |- BOUNDED  ph
21ax-bdn 12942 . . . 4  |- BOUNDED  -.  ph
32ax-bdn 12942 . . 3  |- BOUNDED  -.  -.  ph
43, 1ax-bdim 12939 . 2  |- BOUNDED  ( -.  -.  ph  ->  ph )
5 df-stab 801 . 2  |-  (STAB  ph  <->  ( -.  -.  ph  ->  ph ) )
64, 5bd0r 12950 1  |- BOUNDED STAB  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4  STAB wstab 800  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-bdim 12939  ax-bdn 12942
This theorem depends on definitions:  df-bi 116  df-stab 801
This theorem is referenced by: (None)
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