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Theorem ledior 177
Description: Half of distributive law. (Contributed by NM, 30-Nov-1998.)
Assertion
Ref Expression
ledior ((bc) ∪ a) ≤ ((ba) ∩ (ca))

Proof of Theorem ledior
StepHypRef Expression
1 ledio 176 . 2 (a ∪ (bc)) ≤ ((ab) ∩ (ac))
2 ax-a2 31 . 2 ((bc) ∪ a) = (a ∪ (bc))
3 ax-a2 31 . . 3 (ba) = (ab)
4 ax-a2 31 . . 3 (ca) = (ac)
53, 42an 79 . 2 ((ba) ∩ (ca)) = ((ab) ∩ (ac))
61, 2, 5le3tr1 140 1 ((bc) ∪ a) ≤ ((ba) ∩ (ca))
Colors of variables: term
Syntax hints:  wle 2  wo 6  wa 7
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-le1 130  df-le2 131
This theorem is referenced by:  oadistc0  1021
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