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Theorem oa4cl 1027
Description: 4-variable OA closed equational form. (Contributed by NM, 1-Dec-1998.)
Assertion
Ref Expression
oa4cl ((a ∪ (ba )) ∩ (c ∪ (dc ))) ≤ ((ba ) ∪ (a ∩ (c ∪ ((ac) ∩ ((ba ) ∪ (dc ))))))

Proof of Theorem oa4cl
StepHypRef Expression
1 leor 159 . . 3 a ≤ (ba)
2 oran2 92 . . 3 (ba) = (ba )
31, 2lbtr 139 . 2 a ≤ (ba )
4 leor 159 . . 3 c ≤ (dc)
5 oran2 92 . . 3 (dc) = (dc )
64, 5lbtr 139 . 2 c ≤ (dc )
73, 6ax-oal4 1026 1 ((a ∪ (ba )) ∩ (c ∪ (dc ))) ≤ ((ba ) ∪ (a ∩ (c ∪ ((ac) ∩ ((ba ) ∪ (dc ))))))
Colors of variables: term
Syntax hints:  wle 2   wn 4  wo 6  wa 7
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  ax-oal4 1026
This theorem depends on definitions:  df-a 40  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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