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Theorem ordir 863
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 862 . 2  |-  ( ( ch  \/  ( ph  /\ 
ps ) )  <->  ( ( ch  \/  ph )  /\  ( ch  \/  ps ) ) )
2 orcom 385 . 2  |-  ( ( ( ph  /\  ps )  \/  ch )  <->  ( ch  \/  ( ph  /\ 
ps ) ) )
3 orcom 385 . . 3  |-  ( (
ph  \/  ch )  <->  ( ch  \/  ph )
)
4 orcom 385 . . 3  |-  ( ( ps  \/  ch )  <->  ( ch  \/  ps )
)
53, 4anbi12i 695 . 2  |-  ( ( ( ph  \/  ch )  /\  ( ps  \/  ch ) )  <->  ( ( ch  \/  ph )  /\  ( ch  \/  ps ) ) )
61, 2, 53bitr4i 277 1  |-  ( ( ( ph  /\  ps )  \/  ch )  <->  ( ( ph  \/  ch )  /\  ( ps  \/  ch ) ) )
Colors of variables: wff setvar class
Syntax hints:    <-> wb 184    \/ wo 366    /\ wa 367
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369
This theorem is referenced by:  orddi  867  pm5.62  921  dn1  964  cadan  1462  elnn0z  10873  ifpim123g  38122  rp-fakeanorass  38170
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