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Theorem dp41lemd 1184

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
dp41lemd	c2 a0 b1 c2 c0 c1 c2 c0 c1 c2 a0 b1

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Proof of Theorem dp41lemd

Step	Hyp	Ref	Expression
1		mldual 1122	. 2 c2 a0 b1 c2 c0 c1 c2 a0 b1 c2 c0 c1
2		ancom 74	. . 3 c2 c0 c1 c0 c1 c2
3	2	lor 70	. 2 c2 a0 b1 c2 c0 c1 c2 a0 b1 c0 c1 c2
4		lea 160	. . . 4 c2 a0 b1 c2
5	4	ml2i 1123	. . 3 c2 a0 b1 c0 c1 c2 c2 a0 b1 c0 c1 c2
6		ancom 74	. . 3 c2 a0 b1 c0 c1 c2 c2 c2 a0 b1 c0 c1
7		ax-a2 31	. . . 4 c2 a0 b1 c0 c1 c0 c1 c2 a0 b1
8	7	lan 77	. . 3 c2 c2 a0 b1 c0 c1 c2 c0 c1 c2 a0 b1
9	5, 6, 8	3tr 65	. 2 c2 a0 b1 c0 c1 c2 c2 c0 c1 c2 a0 b1
10	1, 3, 9	3tr 65	1 c2 a0 b1 c2 c0 c1 c2 c0 c1 c2 a0 b1

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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