MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm5.35 Unicode version

Theorem pm5.35 874
Description: Theorem *5.35 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm5.35  |-  ( ( ( ph  ->  ps )  /\  ( ph  ->  ch ) )  ->  ( ph  ->  ( ps  <->  ch )
) )

Proof of Theorem pm5.35
StepHypRef Expression
1 pm5.1 833 . 2  |-  ( ( ( ph  ->  ps )  /\  ( ph  ->  ch ) )  ->  (
( ph  ->  ps )  <->  (
ph  ->  ch ) ) )
21pm5.74rd 241 1  |-  ( ( ( ph  ->  ps )  /\  ( ph  ->  ch ) )  ->  ( ph  ->  ( ps  <->  ch )
) )
Colors of variables: wff set class
Syntax hints:    -> wi 6    <-> wb 178    /\ wa 360
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-an 362
  Copyright terms: Public domain W3C validator