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Theorem oa4lem3 939
Description: Lemma for 3-var to 4-var OA.
Hypotheses
Ref Expression
oa4lem1.1 a =< b'
oa4lem1.2 c =< d'
Assertion
Ref Expression
oa4lem3 ((a v b) ^ (c v d)) =< ((b v d)' v (((a v c)' ->2 b) ^ ((a v c)' ->2 d)))
Proof of Theorem oa4lem3
StepHypRef Expression
1 oa4lem1.1 . . . 4 a =< b'
2 oa4lem1.2 . . . 4 c =< d'
31, 2oa4lem1 937 . . 3 (a v b) =< ((a v c)' ->2 b)
41, 2oa4lem2 938 . . 3 (c v d) =< ((a v c)' ->2 d)
53, 4le2an 169 . 2 ((a v b) ^ (c v d)) =< (((a v c)' ->2 b) ^ ((a v c)' ->2 d))
6 leor 159 . 2 (((a v c)' ->2 b) ^ ((a v c)' ->2 d)) =< ((b v d)' v (((a v c)' ->2 b) ^ ((a v c)' ->2 d)))
75, 6letr 137 1 ((a v b) ^ (c v d)) =< ((b v d)' v (((a v c)' ->2 b) ^ ((a v c)' ->2 d)))
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: (None)
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