MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  pm5.61 Structured version   Unicode version

Theorem pm5.61 710
Description: Theorem *5.61 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 30-Jun-2013.)
Assertion
Ref Expression
pm5.61  |-  ( ( ( ph  \/  ps )  /\  -.  ps )  <->  (
ph  /\  -.  ps )
)

Proof of Theorem pm5.61
StepHypRef Expression
1 biorf 403 . . 3  |-  ( -. 
ps  ->  ( ph  <->  ( ps  \/  ph ) ) )
2 orcom 385 . . 3  |-  ( ( ps  \/  ph )  <->  (
ph  \/  ps )
)
31, 2syl6rbb 262 . 2  |-  ( -. 
ps  ->  ( ( ph  \/  ps )  <->  ph ) )
43pm5.32ri 636 1  |-  ( ( ( ph  \/  ps )  /\  -.  ps )  <->  (
ph  /\  -.  ps )
)
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    <-> wb 184    \/ wo 366    /\ wa 367
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-or 368  df-an 369
This theorem is referenced by:  pm5.75  935  xrnemnf  11331  xrnepnf  11332  hashinfxadd  12439  limcdif  22449  ellimc2  22450  limcmpt  22456  limcres  22459  tglineeltr  24215  tltnle  27887  xrlttri5d  31708
  Copyright terms: Public domain W3C validator