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Theorem negant5 863
Description: Negated antecedent identity.
Hypothesis
Ref Expression
negant.1 (a ->1 c) = (b ->1 c)
Assertion
Ref Expression
negant5 (a' ->5 c) = (b' ->5 c)
Proof of Theorem negant5
StepHypRef Expression
1 negant.1 . . . 4 (a ->1 c) = (b ->1 c)
21negant2 858 . . 3 (a' ->2 c) = (b' ->2 c)
31negant4 862 . . 3 (a' ->4 c) = (b' ->4 c)
42, 32an 79 . 2 ((a' ->2 c) ^ (a' ->4 c)) = ((b' ->2 c) ^ (b' ->4 c))
5 u24lem 770 . 2 ((a' ->2 c) ^ (a' ->4 c)) = (a' ->5 c)
6 u24lem 770 . 2 ((b' ->2 c) ^ (b' ->4 c)) = (b' ->5 c)
74, 5, 63tr2 64 1 (a' ->5 c) = (b' ->5 c)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   ^ wa 7   ->1 wi1 12   ->2 wi2 13   ->4 wi4 15   ->5 wi5 16
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-i1 44  df-i2 45  df-i3 46  df-i4 47  df-i5 48  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
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