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

Theorem bj-stst 13489
Description: Stability of a proposition is stable if and only if that proposition is stable. STAB is idempotent. (Contributed by BJ, 9-Oct-2019.)
Assertion
Ref Expression
bj-stst  |-  (STAB STAB  ph  <-> STAB  ph )

Proof of Theorem bj-stst
StepHypRef Expression
1 bj-nnst 13487 . 2  |-  -.  -. STAB  ph
2 bj-nnbist 13488 . 2  |-  ( -. 
-. STAB  ph  ->  (STAB STAB  ph  <-> STAB  ph )
)
31, 2ax-mp 5 1  |-  (STAB STAB  ph  <-> STAB  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104  STAB wstab 820
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
This theorem depends on definitions:  df-bi 116  df-stab 821
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator