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Theorem orordi 112
Description: Distribution of disjunction over disjunction.
Assertion
Ref Expression
orordi (a v (b v c)) = ((a v b) v (a v c))
Proof of Theorem orordi
StepHypRef Expression
1 oridm 110 . . . 4 (a v a) = a
21ax-r1 35 . . 3 a = (a v a)
32ax-r5 38 . 2 (a v (b v c)) = ((a v a) v (b v c))
4 or4 84 . 2 ((a v a) v (b v c)) = ((a v b) v (a v c))
53, 4ax-r2 36 1 (a v (b v c)) = ((a v b) v (a v c))
Colors of variables: term
Syntax hints:   = wb 1   v wo 6
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-t 41  df-f 42
This theorem is referenced by:  ska2  432  lem4  511  i3abs1  522  u12lem  771  orbi  842  i1orni1  847  lem4.6.6i1j3  1092
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