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Theorem oa4cl 1027
Description: 4-variable OA closed equational form)
Assertion
Ref Expression
oa4cl ((a v (b ^ a')) ^ (c v (d ^ c'))) =< ((b ^ a') v (a ^ (c v ((a v c) ^ ((b ^ a') v (d ^ c'))))))
Proof of Theorem oa4cl
StepHypRef Expression
1 leor 159 . . 3 a =< (b' v a)
2 oran2 92 . . 3 (b' v a) = (b ^ a')'
31, 2lbtr 139 . 2 a =< (b ^ a')'
4 leor 159 . . 3 c =< (d' v c)
5 oran2 92 . . 3 (d' v c) = (d ^ c')'
64, 5lbtr 139 . 2 c =< (d ^ c')'
73, 6ax-oal4 1026 1 ((a v (b ^ a')) ^ (c v (d ^ c'))) =< ((b ^ a') v (a ^ (c v ((a v c) ^ ((b ^ a') v (d ^ c'))))))
Colors of variables: term
Syntax hints:   =< wle 2  'wn 4   v 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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