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Theorem orordir 517
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 500 . . 3  |-  ( ( ch  \/  ch )  <->  ch )
21orbi2i 505 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  ch ) )  <->  ( ( ph  \/  ps )  \/ 
ch ) )
3 or4 514 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  ch ) )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  ch ) ) )
42, 3bitr3i 242 1  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357
This theorem is referenced by:  sspsstri  3278  psslinpr  8655  elznn0  10038  tosso  14142
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
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