Users' Mathboxes Mathbox for Scott Fenton < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >   Mathboxes  >  3orel2 Structured version   Unicode version

Theorem 3orel2 25196
Description: Partial elimination of a triple disjunction by denial of a disjunct. (Contributed by Scott Fenton, 26-Mar-2011.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Assertion
Ref Expression
3orel2  |-  ( -. 
ps  ->  ( ( ph  \/  ps  \/  ch )  ->  ( ph  \/  ch ) ) )

Proof of Theorem 3orel2
StepHypRef Expression
1 3orrot 943 . 2  |-  ( (
ph  \/  ps  \/  ch )  <->  ( ps  \/  ch  \/  ph ) )
2 3orel1 25195 . . 3  |-  ( -. 
ps  ->  ( ( ps  \/  ch  \/  ph )  ->  ( ch  \/  ph ) ) )
3 orcom 378 . . 3  |-  ( ( ch  \/  ph )  <->  (
ph  \/  ch )
)
42, 3syl6ib 219 . 2  |-  ( -. 
ps  ->  ( ( ps  \/  ch  \/  ph )  ->  ( ph  \/  ch ) ) )
51, 4syl5bi 210 1  |-  ( -. 
ps  ->  ( ( ph  \/  ps  \/  ch )  ->  ( ph  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 359    \/ w3o 936
This theorem is referenced by:  nobnddown  25687
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 179  df-or 361  df-3or 938
  Copyright terms: Public domain W3C validator