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Theorem dp41lema 1180

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
dp41lema	a0 b0 a1 b1 a0 b1 c2 c0 c1

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Proof of Theorem dp41lema

Step	Hyp	Ref	Expression
1		dp41lem.5	. . . . . . 7 p2 a0 b0 a1 b1
2	1	cm 61	. . . . . 6 a0 b0 a1 b1 p2
3		dp41lem.6	. . . . . 6 p2 a2 b2
4	2, 3	bltr 138	. . . . 5 a0 b0 a1 b1 a2 b2
5	4	df2le2 136	. . . 4 a0 b0 a1 b1 a2 b2 a0 b0 a1 b1
6	5	cm 61	. . 3 a0 b0 a1 b1 a0 b0 a1 b1 a2 b2
7		dp41lem.4	. . . 4 a0 b0 a1 b1 a2 b2
8	7	cm 61	. . 3 a0 b0 a1 b1 a2 b2
9	6, 8	tr 62	. 2 a0 b0 a1 b1
10		dp41lem.1	. . 3 c0 a1 a2 b1 b2
11		dp41lem.2	. . 3 c1 a0 a2 b0 b2
12		dp41lem.3	. . 3 c2 a0 a1 b0 b1
13	10, 11, 12, 7	dp34 1179	. 2 a0 b1 c2 c0 c1
14	9, 13	bltr 138	1 a0 b0 a1 b1 a0 b1 c2 c0 c1

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-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:  dp41lemc  1183

Copyright terms: Public domain

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