MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm5.14 Unicode version

Theorem pm5.14 861
Description: Theorem *5.14 of [WhiteheadRussell] p. 123. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.14  |-  ( (
ph  ->  ps )  \/  ( ps  ->  ch ) )

Proof of Theorem pm5.14
StepHypRef Expression
1 ax-1 7 . . . 4  |-  ( ps 
->  ( ph  ->  ps ) )
21con3i 129 . . 3  |-  ( -.  ( ph  ->  ps )  ->  -.  ps )
32pm2.21d 100 . 2  |-  ( -.  ( ph  ->  ps )  ->  ( ps  ->  ch ) )
43orri 367 1  |-  ( (
ph  ->  ps )  \/  ( ps  ->  ch ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    \/ wo 359
This theorem is referenced by:  pm5.13  862
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