Theorem oadist12 990

Description: Distributive law derived from OA.

Assertion

Ref	Expression
oadist12	((a ->2 b) ^ (((b v c) ->1 ((a ->2 b) ^ (a ->2 c))) v ((b v c) ->2 ((a ->2 b) ^ (a ->2 c))))) = (((a ->2 b) ^ ((b v c) ->1 ((a ->2 b) ^ (a ->2 c)))) v ((a ->2 b) ^ ((b v c) ->2 ((a ->2 b) ^ (a ->2 c)))))

Proof of Theorem oadist12

Step	Hyp	Ref	Expression
1		u12lem 753	. 2 (((b v c) ->1 ((a ->2 b) ^ (a ->2 c))) v ((b v c) ->2 ((a ->2 b) ^ (a ->2 c)))) = ((b v c) ->0 ((a ->2 b) ^ (a ->2 c)))
2	1	oadist2 989	1 ((a ->2 b) ^ (((b v c) ->1 ((a ->2 b) ^ (a ->2 c))) v ((b v c) ->2 ((a ->2 b) ^ (a ->2 c))))) = (((a ->2 b) ^ ((b v c) ->1 ((a ->2 b) ^ (a ->2 c)))) v ((a ->2 b) ^ ((b v c) ->2 ((a ->2 b) ^ (a ->2 c)))))

Syntax hints:   = wb 1   v wo 6   ^ wa 7   ->1 wi1 13   ->2 wi2 14

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-3oa 978

This theorem depends on definitions:  df-a 39  df-t 40  df-f 41  df-i0 42  df-i1 43  df-i2 44  df-le1 122  df-le2 123

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