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Theorem pm5.61 717
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 406 . . 3  |-  ( -. 
ps  ->  ( ph  <->  ( ps  \/  ph ) ) )
2 orcom 388 . . 3  |-  ( ( ps  \/  ph )  <->  (
ph  \/  ps )
)
31, 2syl6rbb 265 . 2  |-  ( -. 
ps  ->  ( ( ph  \/  ps )  <->  ph ) )
43pm5.32ri 642 1  |-  ( ( ( ph  \/  ps )  /\  -.  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:  pm5.75  945  xrnemnf  11420  xrnepnf  11421  hashinfxadd  12564  limcdif  22818  ellimc2  22819  limcmpt  22825  limcres  22828  tglineeltr  24663  tltnle  28418  icorempt2  31695  poimirlem14  31868  xrlttri5d  37335
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