Theorem 3vth8 793

Description: A 3-variable theorem.

Assertion

Ref	Expression
3vth8	(a ->2 (b v c)) = (((a ->2 b) ^ (c ->2 b)) v ((a ->2 c) ^ (b ->2 c)))

Proof of Theorem 3vth8

Step	Hyp	Ref	Expression
1		3vth7 792	. . 3 ((a ->2 b)_|_ ->2 (b v c)) = (a ->2 (b v c))
2	1	ax-r1 34	. 2 (a ->2 (b v c)) = ((a ->2 b)_|_ ->2 (b v c))
3		3vth6 791	. 2 ((a ->2 b)_|_ ->2 (b v c)) = (((a ->2 b) ^ (c ->2 b)) v ((a ->2 c) ^ (b ->2 c)))
4	2, 3	ax-r2 35	1 (a ->2 (b v c)) = (((a ->2 b) ^ (c ->2 b)) v ((a ->2 c) ^ (b ->2 c)))

Syntax hints:   = wb 1  _|_wn 4   v wo 6   ^ wa 7   ->2 wi2 14

This theorem was proved from axioms:  ax-a1 29  ax-a2 30  ax-a3 31  ax-a4 32  ax-a5 33  ax-r1 34  ax-r2 35  ax-r4 36  ax-r5 37  ax-r3 421

This theorem depends on definitions:  df-b 38  df-a 39  df-t 40  df-f 41  df-i2 44  df-le1 122  df-le2 123  df-c1 124  df-c2 125

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