MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm3.37 Unicode version

Theorem pm3.37 565
Description: Theorem *3.37 (Transp) of [WhiteheadRussell] p. 112. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 23-Oct-2012.)
Assertion
Ref Expression
pm3.37  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ( ph  /\  -.  ch )  ->  -.  ps ) )

Proof of Theorem pm3.37
StepHypRef Expression
1 pm4.14 564 . 2  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ( ph  /\  -.  ch )  ->  -.  ps ) )
21biimpi 188 1  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ( ph  /\  -.  ch )  ->  -.  ps ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    -> wi 6    /\ 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