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

Theorem pm3.37 579
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 pm4.14 578 . 2  |-  ( ( ( ph  /\  ps )  ->  ch )  <->  ( ( ph  /\  -.  ch )  ->  -.  ps ) )
21biimpi 194 1  |-  ( ( ( ph  /\  ps )  ->  ch )  -> 
( ( ph  /\  -.  ch )  ->  -.  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator