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Theorem pm5.63 890
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 404 . . 3  |-  ( ph  \/  -.  ph )
2 ordi 834 . . 3  |-  ( (
ph  \/  ( -.  ph 
/\  ps ) )  <->  ( ( ph  \/  -.  ph )  /\  ( ph  \/  ps ) ) )
31, 2mpbiran 884 . 2  |-  ( (
ph  \/  ( -.  ph 
/\  ps ) )  <->  ( ph  \/  ps ) )
43bicomi 193 1  |-  ( (
ph  \/  ps )  <->  (
ph  \/  ( -.  ph 
/\  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 3    <-> wb 176    \/ wo 357    /\ wa 358
This theorem is referenced by:  cad1  1388  plydivex  19673  lineunray  24180
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 177  df-or 359  df-an 360
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