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Theorem bj-stst 14724
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 14722 . 2  |-  -.  -. STAB  ph
2 bj-nnbist 14723 . 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 105  STAB wstab 831
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616
This theorem depends on definitions:  df-bi 117  df-stab 832
This theorem is referenced by: (None)
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