QLE Home Quantum Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  ud3lem3a GIF version

Theorem ud3lem3a 572
Description: Lemma for unified disjunction.
Assertion
Ref Expression
ud3lem3a ((a3 b) ∩ (ab)) = (a3 b)

Proof of Theorem ud3lem3a
StepHypRef Expression
1 ud3lem0c 279 . . 3 (a3 b) = (((ab ) ∩ (ab)) ∩ (a ∪ (ab )))
2 lea 160 . . . 4 (((ab ) ∩ (ab)) ∩ (a ∪ (ab ))) ≤ ((ab ) ∩ (ab))
3 lear 161 . . . 4 ((ab ) ∩ (ab)) ≤ (ab)
42, 3letr 137 . . 3 (((ab ) ∩ (ab)) ∩ (a ∪ (ab ))) ≤ (ab)
51, 4bltr 138 . 2 (a3 b) ≤ (ab)
65df2le2 136 1 ((a3 b) ∩ (ab)) = (a3 b)
Colors of variables: term
Syntax hints:   = wb 1   wn 4  wo 6  wa 7  3 wi3 14
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-i3 46  df-le1 130  df-le2 131
This theorem is referenced by:  ud3lem3  576
  Copyright terms: Public domain W3C validator