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Theorem negant3 860
Description: Negated antecedent identity.
Hypothesis
Ref Expression
negant.1 (a ->1 c) = (b ->1 c)
Assertion
Ref Expression
negant3 (a' ->3 c) = (b' ->3 c)
Proof of Theorem negant3
StepHypRef Expression
1 negant.1 . . . 4 (a ->1 c) = (b ->1 c)
21sac 835 . . 3 (a' ->1 c) = (b' ->1 c)
32negantlem9 859 . 2 (a' ->3 c) =< (b' ->3 c)
42ax-r1 35 . . 3 (b' ->1 c) = (a' ->1 c)
54negantlem9 859 . 2 (b' ->3 c) =< (a' ->3 c)
63, 5lebi 145 1 (a' ->3 c) = (b' ->3 c)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   ->1 wi1 12   ->3 wi3 14
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-i3 46  df-le1 130  df-le2 131  df-c1 132  df-c2 133
This theorem is referenced by: (None)
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