MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.82 Unicode version

Theorem pm2.82 825
Description: Theorem *2.82 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.82  |-  ( ( ( ph  \/  ps )  \/  ch )  ->  ( ( ( ph  \/  -.  ch )  \/ 
th )  ->  (
( ph  \/  ps )  \/  th )
) )

Proof of Theorem pm2.82
StepHypRef Expression
1 ax-1 5 . . 3  |-  ( (
ph  \/  ps )  ->  ( ( ph  \/  -.  ch )  ->  ( ph  \/  ps ) ) )
2 pm2.24 101 . . . 4  |-  ( ch 
->  ( -.  ch  ->  ps ) )
32orim2d 813 . . 3  |-  ( ch 
->  ( ( ph  \/  -.  ch )  ->  ( ph  \/  ps ) ) )
41, 3jaoi 368 . 2  |-  ( ( ( ph  \/  ps )  \/  ch )  ->  ( ( ph  \/  -.  ch )  ->  ( ph  \/  ps ) ) )
54orim1d 812 1  |-  ( ( ( ph  \/  ps )  \/  ch )  ->  ( ( ( ph  \/  -.  ch )  \/ 
th )  ->  (
( ph  \/  ps )  \/  th )
) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 357
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-an 360
  Copyright terms: Public domain W3C validator