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Theorem ordi 864
Description: Distributive law for disjunction. Theorem *4.41 of [WhiteheadRussell] p. 119. (Contributed by NM, 5-Jan-1993.) (Proof shortened by Andrew Salmon, 7-May-2011.) (Proof shortened by Wolf Lammen, 28-Nov-2013.)
Assertion
Ref Expression
ordi

Proof of Theorem ordi
StepHypRef Expression
1 jcab 863 . 2
2 df-or 370 . 2
3 df-or 370 . . 3
4 df-or 370 . . 3
53, 4anbi12i 697 . 2
61, 2, 53bitr4i 277 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  \/wo 368  /\wa 369
This theorem is referenced by:  ordir  865  orddi  869  pm5.63  924  pm4.43  927  cadan  1459  undi  3744  undif4  3883  elnn1uz2  11187  or3di  27367  bj-ifim123g  37706  bj-ifidg  37707  bj-ifan23  37729
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 370  df-an 371
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