QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  oa6to4h2 Unicode version
Theorem oa6to4h2 956
Description: Satisfaction of 6-variable OA law hypothesis.
Hypotheses
Ref Expression
oa6to4.1 b' = (a ->1 g)'
oa6to4.2 d' = (c ->1 g)'
oa6to4.3 f' = (e ->1 g)'
Assertion
Ref Expression
oa6to4h2 c' =< d''
Proof of Theorem oa6to4h2
StepHypRef Expression
1 leo 158 . 2 c' =< (c' v (c ^ g))
2 oa6to4.2 . . . . 5 d' = (c ->1 g)'
3 df-i1 44 . . . . . 6 (c ->1 g) = (c' v (c ^ g))
43ax-r4 37 . . . . 5 (c ->1 g)' = (c' v (c ^ g))'
52, 4ax-r2 36 . . . 4 d' = (c' v (c ^ g))'
65ax-r1 35 . . 3 (c' v (c ^ g))' = d'
76con3 68 . 2 (c' v (c ^ g)) = d''
81, 7lbtr 139 1 c' =< d''
Colors of variables: term
Syntax hints:   = wb 1   =< wle 2  'wn 4   v wo 6   ^ wa 7   ->1 wi1 12
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38
This theorem depends on definitions:  df-a 40  df-i1 44  df-le1 130  df-le2 131
This theorem is referenced by: (None)
  Copyright terms: Public domain W3C validator