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Theorem orordi 517
Description: Distribution of disjunction over disjunction. (Contributed by NM, 25-Feb-1995.)
Assertion
Ref Expression
orordi  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ( ph  \/  ps )  \/  ( ph  \/  ch ) ) )

Proof of Theorem orordi
StepHypRef Expression
1 oridm 501 . . 3  |-  ( (
ph  \/  ph )  <->  ph )
21orbi1i 507 . 2  |-  ( ( ( ph  \/  ph )  \/  ( ps  \/  ch ) )  <->  ( ph  \/  ( ps  \/  ch ) ) )
3 or4 515 . 2  |-  ( ( ( ph  \/  ph )  \/  ( ps  \/  ch ) )  <->  ( ( ph  \/  ps )  \/  ( ph  \/  ch ) ) )
42, 3bitr3i 243 1  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ( ph  \/  ps )  \/  ( ph  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 177    \/ wo 358
This theorem is referenced by:  pm4.78  566
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 178  df-or 360
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