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Theorem u1lem3var1 731
Description: A 3-variable formula. (Contributed by Josiah Burroughs 26-May-04.)
Assertion
Ref Expression
u1lem3var1 (((a ->1 c) ^ (b ->1 c))' v (((a ->1 c)' ->1 c) ^ ((b ->1 c)' ->1 c))) = 1
Proof of Theorem u1lem3var1
StepHypRef Expression
1 ax-a2 31 . 2 (((a ->1 c) ^ (b ->1 c))' v ((a ->1 c) ^ (b ->1 c))) = (((a ->1 c) ^ (b ->1 c)) v ((a ->1 c) ^ (b ->1 c))')
2 u1lemn1b 730 . . . . 5 (a ->1 c) = ((a ->1 c)' ->1 c)
3 u1lemn1b 730 . . . . 5 (b ->1 c) = ((b ->1 c)' ->1 c)
42, 32an 79 . . . 4 ((a ->1 c) ^ (b ->1 c)) = (((a ->1 c)' ->1 c) ^ ((b ->1 c)' ->1 c))
54ax-r1 35 . . 3 (((a ->1 c)' ->1 c) ^ ((b ->1 c)' ->1 c)) = ((a ->1 c) ^ (b ->1 c))
65lor 70 . 2 (((a ->1 c) ^ (b ->1 c))' v (((a ->1 c)' ->1 c) ^ ((b ->1 c)' ->1 c))) = (((a ->1 c) ^ (b ->1 c))' v ((a ->1 c) ^ (b ->1 c)))
7 df-t 41 . 2 1 = (((a ->1 c) ^ (b ->1 c)) v ((a ->1 c) ^ (b ->1 c))')
81, 6, 73tr1 63 1 (((a ->1 c) ^ (b ->1 c))' v (((a ->1 c)' ->1 c) ^ ((b ->1 c)' ->1 c))) = 1
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7  1wt 8   ->1 wi1 12
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-a 40  df-t 41  df-f 42  df-i1 44
This theorem is referenced by: (None)
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