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Theorem ordir 835
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 834 . 2  |-  ( ( ch  \/  ( ph  /\ 
ps ) )  <->  ( ( ch  \/  ph )  /\  ( ch  \/  ps ) ) )
2 orcom 376 . 2  |-  ( ( ( ph  /\  ps )  \/  ch )  <->  ( ch  \/  ( ph  /\ 
ps ) ) )
3 orcom 376 . . 3  |-  ( (
ph  \/  ch )  <->  ( ch  \/  ph )
)
4 orcom 376 . . 3  |-  ( ( ps  \/  ch )  <->  ( ch  \/  ps )
)
53, 4anbi12i 678 . 2  |-  ( ( ( ph  \/  ch )  /\  ( ps  \/  ch ) )  <->  ( ( ch  \/  ph )  /\  ( ch  \/  ps ) ) )
61, 2, 53bitr4i 268 1  |-  ( ( ( ph  /\  ps )  \/  ch )  <->  ( ( ph  \/  ch )  /\  ( ps  \/  ch ) ) )
Colors of variables: wff set class
Syntax hints:    <-> wb 176    \/ wo 357    /\ wa 358
This theorem is referenced by:  orddi  839  pm5.62  889  dn1  932  cadan  1382  pwundifOLD  4317  elnn0z  10052
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  df-an 360
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