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Theorem bj-trst 12936
Description: A provable formula is stable. (Contributed by BJ, 24-Nov-2023.)
Assertion
Ref Expression
bj-trst  |-  ( ph  -> STAB  ph )

Proof of Theorem bj-trst
StepHypRef Expression
1 ax-1 6 . 2  |-  ( ph  ->  ( -.  -.  ph  ->  ph ) )
2 df-stab 816 . 2  |-  (STAB  ph  <->  ( -.  -.  ph  ->  ph ) )
31, 2sylibr 133 1  |-  ( ph  -> STAB  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4  STAB wstab 815
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem depends on definitions:  df-bi 116  df-stab 816
This theorem is referenced by:  bj-nnbist  12938  bj-dcstab  12946
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