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Theorem bj-dcst 13504
Description: Stability of a proposition is decidable if and only if that proposition is stable. (Contributed by BJ, 24-Nov-2023.)
Assertion
Ref Expression
bj-dcst  |-  (DECID STAB  ph  <-> STAB  ph )

Proof of Theorem bj-dcst
StepHypRef Expression
1 bj-nnst 13487 . 2  |-  -.  -. STAB  ph
2 bj-nnbidc 13500 . 2  |-  ( -. 
-. STAB  ph  ->  (DECID STAB  ph  <-> STAB  ph )
)
31, 2ax-mp 5 1  |-  (DECID STAB  ph  <-> STAB  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104  STAB wstab 820  DECID wdc 824
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-in1 604  ax-in2 605  ax-io 699
This theorem depends on definitions:  df-bi 116  df-stab 821  df-dc 825
This theorem is referenced by: (None)
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