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Theorem pm4.43 898
Description: Theorem *4.43 of [WhiteheadRussell] p. 119. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 26-Nov-2012.)
Assertion
Ref Expression
pm4.43  |-  ( ph  <->  ( ( ph  \/  ps )  /\  ( ph  \/  -.  ps ) ) )

Proof of Theorem pm4.43
StepHypRef Expression
1 pm3.24 857 . . 3  |-  -.  ( ps  /\  -.  ps )
21biorfi 398 . 2  |-  ( ph  <->  (
ph  \/  ( ps  /\ 
-.  ps ) ) )
3 ordi 837 . 2  |-  ( (
ph  \/  ( ps  /\ 
-.  ps ) )  <->  ( ( ph  \/  ps )  /\  ( ph  \/  -.  ps ) ) )
42, 3bitri 242 1  |-  ( ph  <->  ( ( ph  \/  ps )  /\  ( ph  \/  -.  ps ) ) )
Colors of variables: wff set class
Syntax hints:   -. wn 5    <-> wb 178    \/ wo 359    /\ wa 360
This theorem is referenced by:  stoweidlem26  26909
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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