 Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  u1lem9a GIF version

Theorem u1lem9a 777
 Description: Lemma used in study of orthoarguesian law. Equation 4.11 of [MegPav2000] p. 23. This is the first part of the inequality.
Assertion
Ref Expression
u1lem9a (a1 b)a

Proof of Theorem u1lem9a
StepHypRef Expression
1 df-i1 44 . . . 4 (a1 b) = (a ∪ (ab))
21ax-r4 37 . . 3 (a1 b) = (a ∪ (ab))
3 anor1 88 . . . 4 (a ∩ (ab) ) = (a ∪ (ab))
43ax-r1 35 . . 3 (a ∪ (ab)) = (a ∩ (ab) )
52, 4ax-r2 36 . 2 (a1 b) = (a ∩ (ab) )
6 lea 160 . 2 (a ∩ (ab) ) ≤ a
75, 6bltr 138 1 (a1 b)a
 Colors of variables: term Syntax hints:   ≤ 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:  u1lem9ab  779  sadm3  838  oa4uto4g  975  oa4uto4  977  lem4.6.3le1  1082
 Copyright terms: Public domain W3C validator