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Theorem orordir 519
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 502 . . 3  |-  ( ( ch  \/  ch )  <->  ch )
21orbi2i 507 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  ch ) )  <->  ( ( ph  \/  ps )  \/ 
ch ) )
3 or4 516 . 2  |-  ( ( ( ph  \/  ps )  \/  ( ch  \/  ch ) )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  ch ) ) )
42, 3bitr3i 244 1  |-  ( ( ( ph  \/  ps )  \/  ch )  <->  ( ( ph  \/  ch )  \/  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 178    \/ wo 359
This theorem is referenced by:  sspsstri  3451  psslinpr  8910  elznn0  10298  tosso  14467
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 179  df-or 361
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