ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  orordi Unicode version

Theorem orordi 700
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 684 . . 3  |-  ( (
ph  \/  ph )  <->  ph )
21orbi1i 690 . 2  |-  ( ( ( ph  \/  ph )  \/  ( ps  \/  ch ) )  <->  ( ph  \/  ( ps  \/  ch ) ) )
3 or4 698 . 2  |-  ( ( ( ph  \/  ph )  \/  ( ps  \/  ch ) )  <->  ( ( ph  \/  ps )  \/  ( ph  \/  ch ) ) )
42, 3bitr3i 179 1  |-  ( (
ph  \/  ( ps  \/  ch ) )  <->  ( ( ph  \/  ps )  \/  ( ph  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 102    \/ wo 639
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-io 640
This theorem depends on definitions:  df-bi 114
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator