Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  3pm3.2ni Unicode version

Theorem 3pm3.2ni 24079
Description: Triple negated disjuntion introduction. (Contributed by Scott Fenton, 20-Apr-2011.)
Hypotheses
Ref Expression
3pm3.2ni.1  |-  -.  ph
3pm3.2ni.2  |-  -.  ps
3pm3.2ni.3  |-  -.  ch
Assertion
Ref Expression
3pm3.2ni  |-  -.  ( ph  \/  ps  \/  ch )

Proof of Theorem 3pm3.2ni
StepHypRef Expression
1 3pm3.2ni.1 . . . 4  |-  -.  ph
2 3pm3.2ni.2 . . . 4  |-  -.  ps
31, 2pm3.2ni 827 . . 3  |-  -.  ( ph  \/  ps )
4 3pm3.2ni.3 . . 3  |-  -.  ch
53, 4pm3.2ni 827 . 2  |-  -.  (
( ph  \/  ps )  \/  ch )
6 df-3or 935 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ( ph  \/  ps )  \/  ch ) )
75, 6mtbir 290 1  |-  -.  ( ph  \/  ps  \/  ch )
Colors of variables: wff set class
Syntax hints:   -. wn 3    \/ wo 357    \/ w3o 933
This theorem is referenced by:  sltsolem1  24393
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 177  df-or 359  df-3or 935
  Copyright terms: Public domain W3C validator