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Theorem orordir 748
Description: Distribution of disjunction over disjunction. (Contributed by NM, 25-Feb-1995.)
Assertion
Ref Expression
orordir  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  ch ) ) )

Proof of Theorem orordir
StepHypRef Expression
1 oridm 731 . . 3  |-  ( ( ch  \/  ch )  <->  ch )
21orbi2i 736 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  ch ) )  <->  ( ( ph  \/  ps )  \/ 
ch ) )
3 or4 745 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  ch ) )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  ch ) ) )
42, 3bitr3i 185 1  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 104    \/ wo 682
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 683
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  elznn0  9037
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