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Theorem oa4lem1 937
 Description: Lemma for 3-var to 4-var OA.
Hypotheses
Ref Expression
oa4lem1.1 ab
oa4lem1.2 cd
Assertion
Ref Expression
oa4lem1 (ab) ≤ ((ac)2 b)

Proof of Theorem oa4lem1
StepHypRef Expression
1 leo 158 . . . . 5 a ≤ (ac)
2 ax-a1 30 . . . . 5 (ac) = (ac)
31, 2lbtr 139 . . . 4 a ≤ (ac)
4 oa4lem1.1 . . . 4 ab
53, 4ler2an 173 . . 3 a ≤ ((ac) b )
65lelor 166 . 2 (ba) ≤ (b ∪ ((ac) b ))
7 ax-a2 31 . 2 (ab) = (ba)
8 df-i2 45 . 2 ((ac)2 b) = (b ∪ ((ac) b ))
96, 7, 8le3tr1 140 1 (ab) ≤ ((ac)2 b)
 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:  oa4lem3  939
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