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Theorem oa4lem3 939
 Description: Lemma for 3-var to 4-var OA.
Hypotheses
Ref Expression
oa4lem1.1 ab
oa4lem1.2 cd
Assertion
Ref Expression
oa4lem3 ((ab) ∩ (cd)) ≤ ((bd) ∪ (((ac)2 b) ∩ ((ac)2 d)))

Proof of Theorem oa4lem3
StepHypRef Expression
1 oa4lem1.1 . . . 4 ab
2 oa4lem1.2 . . . 4 cd
31, 2oa4lem1 937 . . 3 (ab) ≤ ((ac)2 b)
41, 2oa4lem2 938 . . 3 (cd) ≤ ((ac)2 d)
53, 4le2an 169 . 2 ((ab) ∩ (cd)) ≤ (((ac)2 b) ∩ ((ac)2 d))
6 leor 159 . 2 (((ac)2 b) ∩ ((ac)2 d)) ≤ ((bd) ∪ (((ac)2 b) ∩ ((ac)2 d)))
75, 6letr 137 1 ((ab) ∩ (cd)) ≤ ((bd) ∪ (((ac)2 b) ∩ ((ac)2 d)))
 Colors of variables: term Syntax hints:   ≤ wle 2  ⊥ wn 4   ∪ wo 6   ∩ wa 7   →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-i2 45  df-le1 130  df-le2 131 This theorem is referenced by: (None)
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