MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm4.42 Structured version   Unicode version

Theorem pm4.42 968
Description: Theorem *4.42 of [WhiteheadRussell] p. 119. See also ifpid 1433. (Contributed by Roy F. Longton, 21-Jun-2005.)
Assertion
Ref Expression
pm4.42  |-  ( ph  <->  ( ( ph  /\  ps )  \/  ( ph  /\ 
-.  ps ) ) )

Proof of Theorem pm4.42
StepHypRef Expression
1 dedlema 962 . 2  |-  ( ps 
->  ( ph  <->  ( ( ph  /\  ps )  \/  ( ph  /\  -.  ps ) ) ) )
2 dedlemb 963 . 2  |-  ( -. 
ps  ->  ( ph  <->  ( ( ph  /\  ps )  \/  ( ph  /\  -.  ps ) ) ) )
31, 2pm2.61i 167 1  |-  ( ph  <->  ( ( ph  /\  ps )  \/  ( ph  /\ 
-.  ps ) ) )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 187    \/ 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:  inundif  3873  numclwwlk3lem  25819  elim2ifim  28149  smatrcl  28615  expdioph  35795
  Copyright terms: Public domain W3C validator