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Theorem pm5.63 895
Description: Theorem *5.63 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 25-Dec-2012.)
Assertion
Ref Expression
pm5.63  |-  ( (
ph  \/  ps )  <->  (
ph  \/  ( -.  ph 
/\  ps ) ) )

Proof of Theorem pm5.63
StepHypRef Expression
1 exmid 406 . . 3  |-  ( ph  \/  -.  ph )
2 ordi 837 . . 3  |-  ( (
ph  \/  ( -.  ph 
/\  ps ) )  <->  ( ( ph  \/  -.  ph )  /\  ( ph  \/  ps ) ) )
31, 2mpbiran 889 . 2  |-  ( (
ph  \/  ( -.  ph 
/\  ps ) )  <->  ( ph  \/  ps ) )
43bicomi 195 1  |-  ( (
ph  \/  ps )  <->  (
ph  \/  ( -.  ph 
/\  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178    \/ wo 359    /\ wa 360
This theorem is referenced by:  cad1  1394  plydivex  19604  lineunray  24110
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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