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Theorem pm5.61 696
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 396 . . 3  |-  ( -. 
ps  ->  ( ph  <->  ( ps  \/  ph ) ) )
2 orcom 378 . . 3  |-  ( ( ps  \/  ph )  <->  (
ph  \/  ps )
)
31, 2syl6rbb 255 . 2  |-  ( -. 
ps  ->  ( ( ph  \/  ps )  <->  ph ) )
43pm5.32ri 622 1  |-  ( ( ( ph  \/  ps )  /\  -.  ps )  <->  (
ph  /\  -.  ps )
)
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178    \/ wo 359    /\ wa 360
This theorem is referenced by:  pm5.75  908  xrnemnf  10392  xrnepnf  10393  limcdif  19153  ellimc2  19154  limcmpt  19160  limcres  19163  fordisxex  24285
This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362
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