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Theorem negant0 857
 Description: Negated antecedent identity. (Contributed by NM, 6-Aug-2001.)
Hypothesis
Ref Expression
negant.1 (a1 c) = (b1 c)
Assertion
Ref Expression
negant0 (a0 c) = (b0 c)

Proof of Theorem negant0
StepHypRef Expression
1 negant.1 . . . 4 (a1 c) = (b1 c)
21negantlem7 855 . . 3 (ac) = (bc)
3 ax-a1 30 . . . 4 a = a
43ax-r5 38 . . 3 (ac) = (a c)
5 ax-a1 30 . . . 4 b = b
65ax-r5 38 . . 3 (bc) = (b c)
72, 4, 63tr2 64 . 2 (a c) = (b c)
8 df-i0 43 . 2 (a0 c) = (a c)
9 df-i0 43 . 2 (b0 c) = (b c)
107, 8, 93tr1 63 1 (a0 c) = (b0 c)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   →0 wi0 11   →1 wi1 12 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-i0 43  df-i1 44  df-le1 130  df-le2 131  df-c1 132  df-c2 133 This theorem is referenced by: (None)
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