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Theorem orordir 724
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 707 . . 3  |-  ( ( ch  \/  ch )  <->  ch )
21orbi2i 712 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  ch ) )  <->  ( ( ph  \/  ps )  \/ 
ch ) )
3 or4 721 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  ch ) )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  ch ) ) )
42, 3bitr3i 184 1  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 103    \/ wo 662
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663
This theorem depends on definitions:  df-bi 115
This theorem is referenced by:  elznn0  8447
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