MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm3.11 Structured version   Unicode version

Theorem pm3.11 501
Description: Theorem *3.11 of [WhiteheadRussell] p. 111. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm3.11  |-  ( -.  ( -.  ph  \/  -.  ps )  ->  ( ph  /\  ps ) )

Proof of Theorem pm3.11
StepHypRef Expression
1 anor 491 . 2  |-  ( (
ph  /\  ps )  <->  -.  ( -.  ph  \/  -.  ps ) )
21biimpri 209 1  |-  ( -.  ( -.  ph  \/  -.  ps )  ->  ( ph  /\  ps ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4    \/ wo 369    /\ wa 370
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 188  df-or 371  df-an 372
This theorem is referenced by:  pm3.12  502  pm3.13  503  ecased  952
  Copyright terms: Public domain W3C validator