QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  3vth3 Unicode version
Theorem 3vth3 806
Description: A 3-variable theorem. Equivalent to OML.
Assertion
Ref Expression
3vth3 ((a ->2 c) v ((a ->2 b) ^ (b v c)')) = (a ->2 c)
Proof of Theorem 3vth3
StepHypRef Expression
1 ax-a2 31 . 2 ((a ->2 c) v ((a ->2 b) ^ (b v c)')) = (((a ->2 b) ^ (b v c)') v (a ->2 c))
2 3vth1 804 . . 3 ((a ->2 b) ^ (b v c)') =< (a ->2 c)
32df-le2 131 . 2 (((a ->2 b) ^ (b v c)') v (a ->2 c)) = (a ->2 c)
41, 3ax-r2 36 1 ((a ->2 c) v ((a ->2 b) ^ (b v c)')) = (a ->2 c)
Colors of variables: term
Syntax hints:   = wb 1  'wn 4   v wo 6   ^ wa 7   ->2 wi2 13
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  ax-r3 439
This theorem depends on definitions:  df-b 39  df-a 40  df-t 41  df-f 42  df-i2 45  df-le1 130  df-le2 131
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator