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Theorem dp41lemk 1190

Description: Part of proof (4)=>(1) in Day/Pickering 1982.

Hypotheses

Ref	Expression
dp41lem.1	c0 a1 a2 b1 b2
dp41lem.2	c1 a0 a2 b0 b2
dp41lem.3	c2 a0 a1 b0 b1
dp41lem.4	a0 b0 a1 b1 a2 b2
dp41lem.5	p2 a0 b0 a1 b1
dp41lem.6	p2 a2 b2

Assertion

Ref	Expression
dp41lemk	b1 b2 a1 a2 b2 a0 a2 a0 a2 b0 b2 a2 b1 b2 c0 b2 a0 a2 c1 a2 b1 b2

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Proof of Theorem dp41lemk

Step	Hyp	Ref	Expression
1		leao3 164	. . . 4 b2 a0 a2 b1 b2
2	1	mldual2i 1125	. . 3 b1 b2 a1 a2 b2 a0 a2 b1 b2 a1 a2 b2 a0 a2
3		dp41lem.1	. . . . . 6 c0 a1 a2 b1 b2
4		ancom 74	. . . . . 6 a1 a2 b1 b2 b1 b2 a1 a2
5	3, 4	tr 62	. . . . 5 c0 b1 b2 a1 a2
6	5	ror 71	. . . 4 c0 b2 a0 a2 b1 b2 a1 a2 b2 a0 a2
7	6	cm 61	. . 3 b1 b2 a1 a2 b2 a0 a2 c0 b2 a0 a2
8	2, 7	tr 62	. 2 b1 b2 a1 a2 b2 a0 a2 c0 b2 a0 a2
9		leao3 164	. . . 4 a2 b1 b2 a0 a2
10	9	mldual2i 1125	. . 3 a0 a2 b0 b2 a2 b1 b2 a0 a2 b0 b2 a2 b1 b2
11		dp41lem.2	. . . . 5 c1 a0 a2 b0 b2
12	11	ror 71	. . . 4 c1 a2 b1 b2 a0 a2 b0 b2 a2 b1 b2
13	12	cm 61	. . 3 a0 a2 b0 b2 a2 b1 b2 c1 a2 b1 b2
14	10, 13	tr 62	. 2 a0 a2 b0 b2 a2 b1 b2 c1 a2 b1 b2
15	8, 14	2or 72	1 b1 b2 a1 a2 b2 a0 a2 a0 a2 b0 b2 a2 b1 b2 c0 b2 a0 a2 c1 a2 b1 b2

Colors of variables: term

Syntax hints:   wb 1   wle 2   wo 6   wa 7

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  ax-ml 1120

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:  dp41lemm  1192

Copyright terms: Public domain

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