Users' Mathboxes Mathbox for BJ < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >   Mathboxes  >  bj-dcst Unicode version

Theorem bj-dcst 13796
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 13778 . 2  |-  -.  -. STAB  ph
2 bj-nnbidc 13792 . 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 825  DECID wdc 829
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 609  ax-in2 610  ax-io 704
This theorem depends on definitions:  df-bi 116  df-stab 826  df-dc 830
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator