MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.83 Unicode version

Theorem pm2.83 71
Description: Theorem *2.83 of [WhiteheadRussell] p. 108. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm2.83  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  ->  ( ch 
->  th ) )  -> 
( ph  ->  ( ps 
->  th ) ) ) )

Proof of Theorem pm2.83
StepHypRef Expression
1 imim1 70 . 2  |-  ( ( ps  ->  ch )  ->  ( ( ch  ->  th )  ->  ( ps  ->  th ) ) )
21imim3i 55 1  |-  ( (
ph  ->  ( ps  ->  ch ) )  ->  (
( ph  ->  ( ch 
->  th ) )  -> 
( ph  ->  ( ps 
->  th ) ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4
This theorem is referenced by:  rexrsb  27947
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 8
  Copyright terms: Public domain W3C validator