Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  3orel1 Unicode version

Theorem 3orel1 23472
Description: Partial elimination of a triple disjunction by denial of a disjunct. (Contributed by Scott Fenton, 26-Mar-2011.)
Assertion
Ref Expression
3orel1  |-  ( -. 
ph  ->  ( ( ph  \/  ps  \/  ch )  ->  ( ps  \/  ch ) ) )

Proof of Theorem 3orel1
StepHypRef Expression
1 3orass 937 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ph  \/  ( ps  \/  ch ) ) )
2 orel1 371 . 2  |-  ( -. 
ph  ->  ( ( ph  \/  ( ps  \/  ch ) )  ->  ( ps  \/  ch ) ) )
31, 2syl5bi 208 1  |-  ( -. 
ph  ->  ( ( ph  \/  ps  \/  ch )  ->  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357    \/ w3o 933
This theorem is referenced by:  3orel2  23473
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