 Quantum Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  QLE Home  >  Th. List  >  lem4.6.6i2j0 GIF version

Theorem lem4.6.6i2j0 1093
 Description: Equation 4.14 of [MegPav2000] p. 23. The variable i in the paper is set to 2, and j is set to 0. (Contributed by Roy F. Longton, 3-Jul-05.)
Assertion
Ref Expression
lem4.6.6i2j0 ((a2 b) ∪ (a0 b)) = (a0 b)

Proof of Theorem lem4.6.6i2j0
StepHypRef Expression
1 leor 159 . . . 4 b ≤ (ab)
2 leao1 162 . . . 4 (ab ) ≤ (ab)
31, 2lel2or 170 . . 3 (b ∪ (ab )) ≤ (ab)
43df-le2 131 . 2 ((b ∪ (ab )) ∪ (ab)) = (ab)
5 df-i2 45 . . 3 (a2 b) = (b ∪ (ab ))
6 df-i0 43 . . 3 (a0 b) = (ab)
75, 62or 72 . 2 ((a2 b) ∪ (a0 b)) = ((b ∪ (ab )) ∪ (ab))
84, 7, 63tr1 63 1 ((a2 b) ∪ (a0 b)) = (a0 b)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →0 wi0 11   →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 This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-i0 43  df-i2 45  df-le1 130  df-le2 131 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator