QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  negant0 Unicode version
Theorem negant0 857
Description: Negated antecedent identity.
Hypothesis
Ref Expression
negant.1 (a ->1 c) = (b ->1 c)
Assertion
Ref Expression
negant0 (a' ->0 c) = (b' ->0 c)
Proof of Theorem negant0
StepHypRef Expression
1 negant.1 . . . 4 (a ->1 c) = (b ->1 c)
21negantlem7 855 . . 3 (a v c) = (b v c)
3 ax-a1 30 . . . 4 a = a''
43ax-r5 38 . . 3 (a v c) = (a'' v c)
5 ax-a1 30 . . . 4 b = b''
65ax-r5 38 . . 3 (b v c) = (b'' v c)
72, 4, 63tr2 64 . 2 (a'' v c) = (b'' v c)
8 df-i0 43 . 2 (a' ->0 c) = (a'' v c)
9 df-i0 43 . 2 (b' ->0 c) = (b'' v c)
107, 8, 93tr1 63 1 (a' ->0 c) = (b' ->0 c)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v 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)
  Copyright terms: Public domain W3C validator