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Theorem ordir 806
Description: Distributive law for disjunction. (Contributed by NM, 12-Aug-1994.)
Assertion
Ref Expression
ordir  |-  ( ( ( ph  /\  ps )  \/  ch )  <->  ( ( ph  \/  ch )  /\  ( ps  \/  ch ) ) )

Proof of Theorem ordir
StepHypRef Expression
1 ordi 805 . 2  |-  ( ( ch  \/  ( ph  /\ 
ps ) )  <->  ( ( ch  \/  ph )  /\  ( ch  \/  ps ) ) )
2 orcom 717 . 2  |-  ( ( ( ph  /\  ps )  \/  ch )  <->  ( ch  \/  ( ph  /\ 
ps ) ) )
3 orcom 717 . . 3  |-  ( (
ph  \/  ch )  <->  ( ch  \/  ph )
)
4 orcom 717 . . 3  |-  ( ( ps  \/  ch )  <->  ( ch  \/  ps )
)
53, 4anbi12i 455 . 2  |-  ( ( ( ph  \/  ch )  /\  ( ps  \/  ch ) )  <->  ( ( ch  \/  ph )  /\  ( ch  \/  ps ) ) )
61, 2, 53bitr4i 211 1  |-  ( ( ( ph  /\  ps )  \/  ch )  <->  ( ( ph  \/  ch )  /\  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    /\ wa 103    <-> wb 104    \/ wo 697
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698
This theorem depends on definitions:  df-bi 116
This theorem is referenced by:  orddi  809  pm5.62dc  929  dn1dc  944  suc11g  4467  bj-peano4  13142
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