MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.85 Unicode version

Theorem pm2.85 829
Description: Theorem *2.85 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 5-Jan-2013.)
Assertion
Ref Expression
pm2.85  |-  ( ( ( ph  \/  ps )  ->  ( ph  \/  ch ) )  ->  ( ph  \/  ( ps  ->  ch ) ) )

Proof of Theorem pm2.85
StepHypRef Expression
1 orimdi 823 . 2  |-  ( (
ph  \/  ( ps  ->  ch ) )  <->  ( ( ph  \/  ps )  -> 
( ph  \/  ch ) ) )
21biimpri 199 1  |-  ( ( ( ph  \/  ps )  ->  ( ph  \/  ch ) )  ->  ( ph  \/  ( ps  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    \/ wo 359
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361
  Copyright terms: Public domain W3C validator