MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm2.86 Unicode version

Theorem pm2.86 96
Description: Converse of axiom ax-2 8. Theorem *2.86 of [WhiteheadRussell] p. 108. (Contributed by NM, 25-Apr-1994.) (Proof shortened by Wolf Lammen, 3-Apr-2013.)
Assertion
Ref Expression
pm2.86  |-  ( ( ( ph  ->  ps )  ->  ( ph  ->  ch ) )  ->  ( ph  ->  ( ps  ->  ch ) ) )

Proof of Theorem pm2.86
StepHypRef Expression
1 id 21 . 2  |-  ( ( ( ph  ->  ps )  ->  ( ph  ->  ch ) )  ->  (
( ph  ->  ps )  ->  ( ph  ->  ch ) ) )
21pm2.86d 95 1  |-  ( ( ( ph  ->  ps )  ->  ( ph  ->  ch ) )  ->  ( ph  ->  ( ps  ->  ch ) ) )
Colors of variables: wff set class
Syntax hints:    -> wi 6
This theorem is referenced by:  imdi  354
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-mp 10
  Copyright terms: Public domain W3C validator