MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm4.44 Unicode version

Theorem pm4.44 561
Description: Theorem *4.44 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.)
Assertion
Ref Expression
pm4.44  |-  ( ph  <->  (
ph  \/  ( ph  /\ 
ps ) ) )

Proof of Theorem pm4.44
StepHypRef Expression
1 orc 375 . 2  |-  ( ph  ->  ( ph  \/  ( ph  /\  ps ) ) )
2 id 20 . . 3  |-  ( ph  ->  ph )
3 simpl 444 . . 3  |-  ( (
ph  /\  ps )  ->  ph )
42, 3jaoi 369 . 2  |-  ( (
ph  \/  ( ph  /\ 
ps ) )  ->  ph )
51, 4impbii 181 1  |-  ( ph  <->  (
ph  \/  ( ph  /\ 
ps ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    \/ wo 358    /\ wa 359
This theorem is referenced by:  jaoi2  934
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361
  Copyright terms: Public domain W3C validator