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Theorem lem4.6.6i4j0 1098
 Description: Equation 4.14 of [MegPav2000] p. 23. The variable i in the paper is set to 4, and j is set to 0. (Contributed by Roy F. Longton, 3-Jul-05.)
Assertion
Ref Expression
lem4.6.6i4j0 ((a4 b) ∪ (a0 b)) = (a0 b)

Proof of Theorem lem4.6.6i4j0
StepHypRef Expression
1 leao4 165 . . . . 5 (ab) ≤ (ab)
2 leao1 162 . . . . 5 (ab) ≤ (ab)
31, 2lel2or 170 . . . 4 ((ab) ∪ (ab)) ≤ (ab)
4 lea 160 . . . 4 ((ab) ∩ b ) ≤ (ab)
53, 4lel2or 170 . . 3 (((ab) ∪ (ab)) ∪ ((ab) ∩ b )) ≤ (ab)
65df-le2 131 . 2 ((((ab) ∪ (ab)) ∪ ((ab) ∩ b )) ∪ (ab)) = (ab)
7 df-i4 47 . . 3 (a4 b) = (((ab) ∪ (ab)) ∪ ((ab) ∩ b ))
8 df-i0 43 . . 3 (a0 b) = (ab)
97, 82or 72 . 2 ((a4 b) ∪ (a0 b)) = ((((ab) ∪ (ab)) ∪ ((ab) ∩ b )) ∪ (ab))
106, 9, 83tr1 63 1 ((a4 b) ∪ (a0 b)) = (a0 b)
 Colors of variables: term Syntax hints:   = wb 1  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →0 wi0 11   →4 wi4 15 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-i4 47  df-le1 130  df-le2 131 This theorem is referenced by: (None)
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