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

Theorem stabnot 823
Description: Every negated formula is stable. (Contributed by David A. Wheeler, 13-Aug-2018.)
Assertion
Ref Expression
stabnot  |- STAB  -.  ph

Proof of Theorem stabnot
StepHypRef Expression
1 notnotnot 624 . . 3  |-  ( -. 
-.  -.  ph  <->  -.  ph )
21biimpi 119 . 2  |-  ( -. 
-.  -.  ph  ->  -.  ph )
3 df-stab 821 . 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 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:  dcnn  838  cnstab  8543
  Copyright terms: Public domain W3C validator