ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  stabnot Unicode version

Theorem stabnot 779
Description: Every formula of the form  -.  ph is stable. Uses notnotnot 664. (Contributed by David A. Wheeler, 13-Aug-2018.)
Assertion
Ref Expression
stabnot  |- STAB  -.  ph

Proof of Theorem stabnot
StepHypRef Expression
1 notnotnot 664 . . 3  |-  ( -. 
-.  -.  ph  <->  -.  ph )
21biimpi 119 . 2  |-  ( -. 
-.  -.  ph  ->  -.  ph )
3 df-stab 777 . 2  |-  (STAB  -.  ph  <->  ( -.  -.  -.  ph  ->  -.  ph ) )
42, 3mpbir 145 1  |- STAB  -.  ph
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4  STAB wstab 776
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581
This theorem depends on definitions:  df-bi 116  df-stab 777
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator