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

Theorem notnotnot 664
Description: Triple negation. (Contributed by Jim Kingdon, 28-Jul-2018.)
Assertion
Ref Expression
notnotnot  |-  ( -. 
-.  -.  ph  <->  -.  ph )

Proof of Theorem notnotnot
StepHypRef Expression
1 notnot 595 . . 3  |-  ( ph  ->  -.  -.  ph )
21con3i 598 . 2  |-  ( -. 
-.  -.  ph  ->  -.  ph )
3 notnot 595 . 2  |-  ( -. 
ph  ->  -.  -.  -.  ph )
42, 3impbii 125 1  |-  ( -. 
-.  -.  ph  <->  -.  ph )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 104
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia2 106  ax-ia3 107  ax-in1 580  ax-in2 581
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  stabnot  779  testbitestn  862
  Copyright terms: Public domain W3C validator