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

Step	Hyp	Ref	Expression
1		oridm 110	. . . 4 (a v a) = a
2	1	ax-r1 35	. . 3 a = (a v a)
3	2	ax-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))
5	3, 4	ax-r2 36	1 (a v (b v c)) = ((a v b) v (a v c))

Syntax hints:   = wb 1   v wo 6

This theorem is referenced by:  ska2 432  lem4 511  i3abs1 522  u12lem 771  orbi 842  i1orni1 847  lem4.6.6i1j3 1092

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

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