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Theorem oadp35lemf 1208
Description: Part of proof (3)=>(5) in Day/Pickering 1982.
Hypotheses
Ref Expression
oadp35lem.1 c0 = ((a1 v a2) ^ (b1 v b2))
oadp35lem.2 c1 = ((a0 v a2) ^ (b0 v b2))
oadp35lem.3 c2 = ((a0 v a1) ^ (b0 v b1))
oadp35lem.4 p0 = ((a1 v b1) ^ (a2 v b2))
oadp35lem.5 p = (((a0 v b0) ^ (a1 v b1)) ^ (a2 v b2))
Assertion
Ref Expression
oadp35lemf (a0 v p) =< (a0 v (b0 ^ (b1 v (c2 ^ (c0 v c1)))))

Proof of Theorem oadp35lemf
StepHypRef Expression
1 leo 158 . 2 a0 =< (a0 v (b0 ^ (b1 v (c2 ^ (c0 v c1)))))
2 oadp35lem.1 . . 3 c0 = ((a1 v a2) ^ (b1 v b2))
3 oadp35lem.2 . . 3 c1 = ((a0 v a2) ^ (b0 v b2))
4 oadp35lem.3 . . 3 c2 = ((a0 v a1) ^ (b0 v b1))
5 oadp35lem.4 . . 3 p0 = ((a1 v b1) ^ (a2 v b2))
6 oadp35lem.5 . . 3 p = (((a0 v b0) ^ (a1 v b1)) ^ (a2 v b2))
72, 3, 4, 5, 6oadp35lemg 1207 . 2 p =< (a0 v (b0 ^ (b1 v (c2 ^ (c0 v c1)))))
81, 7lel2or 170 1 (a0 v p) =< (a0 v (b0 ^ (b1 v (c2 ^ (c0 v c1)))))
Colors of variables: term
Syntax hints:   = wb 1   =< wle 2   v wo 6   ^ wa 7
This theorem was proved from axioms:  ax-a1 30  ax-a2 31  ax-a3 32  ax-a4 33  ax-a5 34  ax-r1 35  ax-r2 36  ax-r4 37  ax-r5 38  ax-ml 1120  ax-arg 1151
This theorem depends on definitions:  df-a 40  df-t 41  df-f 42  df-le1 130  df-le2 131
This theorem is referenced by: (None)
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