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Theorem oa4lem1 937
Description: Lemma for 3-var to 4-var OA.
Hypotheses
Ref Expression
oa4lem1.1 a =< b'
oa4lem1.2 c =< d'
Assertion
Ref Expression
oa4lem1 (a v b) =< ((a v c)' ->2 b)
Proof of Theorem oa4lem1
StepHypRef Expression
1 leo 158 . . . . 5 a =< (a v c)
2 ax-a1 30 . . . . 5 (a v c) = (a v c)''
31, 2lbtr 139 . . . 4 a =< (a v c)''
4 oa4lem1.1 . . . 4 a =< b'
53, 4ler2an 173 . . 3 a =< ((a v c)'' ^ b')
65lelor 166 . 2 (b v a) =< (b v ((a v c)'' ^ b'))
7 ax-a2 31 . 2 (a v b) = (b v a)
8 df-i2 45 . 2 ((a v c)' ->2 b) = (b v ((a v c)'' ^ b'))
96, 7, 8le3tr1 140 1 (a v b) =< ((a v c)' ->2 b)
Colors of variables: term
Syntax hints:   =< wle 2  'wn 4   v 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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