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Theorem 3vth8 811
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
StepHypRef Expression
1 3vth7 810 . . 3 ((a ->2 b)' ->2 (b v c)) = (a ->2 (b v c))
21ax-r1 35 . 2 (a ->2 (b v c)) = ((a ->2 b)' ->2 (b v c))
3 3vth6 809 . 2 ((a ->2 b)' ->2 (b v c)) = (((a ->2 b) ^ (c ->2 b)) v ((a ->2 c) ^ (b ->2 c)))
42, 3ax-r2 36 1 (a ->2 (b v c)) = (((a ->2 b) ^ (c ->2 b)) v ((a ->2 c) ^ (b ->2 c)))
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->2 wi2 13
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i2 45  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
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