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Theorem pm5.63 891
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 405 . . 3  |-  ( ph  \/  -.  ph )
2 ordi 835 . . 3  |-  ( (
ph  \/  ( -.  ph 
/\  ps ) )  <->  ( ( ph  \/  -.  ph )  /\  ( ph  \/  ps ) ) )
31, 2mpbiran 885 . 2  |-  ( (
ph  \/  ( -.  ph 
/\  ps ) )  <->  ( ph  \/  ps ) )
43bicomi 194 1  |-  ( (
ph  \/  ps )  <->  (
ph  \/  ( -.  ph 
/\  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 177    \/ wo 358    /\ wa 359
This theorem is referenced by:  cad1  1404  plydivex  20167  lineunray  25985
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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