 Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  oa6to4h1 GIF version

Theorem oa6to4h1 955
 Description: Satisfaction of 6-variable OA law hypothesis. (Contributed by NM, 22-Dec-1998.)
Hypotheses
Ref Expression
oa6to4.1 b = (a1 g)
oa6to4.2 d = (c1 g)
oa6to4.3 f = (e1 g)
Assertion
Ref Expression
oa6to4h1 ab

Proof of Theorem oa6to4h1
StepHypRef Expression
1 leo 158 . 2 a ≤ (a ∪ (ag))
2 oa6to4.1 . . . . 5 b = (a1 g)
3 df-i1 44 . . . . . 6 (a1 g) = (a ∪ (ag))
43ax-r4 37 . . . . 5 (a1 g) = (a ∪ (ag))
52, 4ax-r2 36 . . . 4 b = (a ∪ (ag))
65ax-r1 35 . . 3 (a ∪ (ag)) = b
76con3 68 . 2 (a ∪ (ag)) = b
81, 7lbtr 139 1 ab
 Colors of variables: term Syntax hints:   = wb 1   ≤ wle 2  ⊥ wn 4   ∪ 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