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Theorem pm5.61 694
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 395 . . 3  |-  ( -. 
ps  ->  ( ph  <->  ( ps  \/  ph ) ) )
2 orcom 377 . . 3  |-  ( ( ps  \/  ph )  <->  (
ph  \/  ps )
)
31, 2syl6rbb 254 . 2  |-  ( -. 
ps  ->  ( ( ph  \/  ps )  <->  ph ) )
43pm5.32ri 620 1  |-  ( ( ( ph  \/  ps )  /\  -.  ps )  <->  (
ph  /\  -.  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    \/ wo 358    /\ wa 359
This theorem is referenced by:  pm5.75  904  xrnemnf  10718  xrnepnf  10719  hashinfxadd  11659  limcdif  19763  ellimc2  19764  limcmpt  19770  limcres  19773  tltnle  24190
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
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