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Theorem dp53lemd 1164

Description: Part of proof (5)=>(3) in Day/Pickering 1982.

Hypotheses

Ref	Expression
dp53lem.1	c0 a1 a2 b1 b2
dp53lem.2	c1 a0 a2 b0 b2
dp53lem.3	c2 a0 a1 b0 b1
dp53lem.4	p0 a1 b1 a2 b2
dp53lem.5	a0 b0 a1 b1 a2 b2

Assertion

Ref	Expression
dp53lemd	b0 a0 p0 b0 a0 b0 b1 c2 c0 c1

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Proof of Theorem dp53lemd

Step	Hyp	Ref	Expression
1		lea 160	. . 3 b0 a0 p0 b0
2		leor 159	. . . 4 b0 a0 p0 b1 b0 a0 p0
3		dp53lem.1	. . . . 5 c0 a1 a2 b1 b2
4		dp53lem.2	. . . . 5 c1 a0 a2 b0 b2
5		dp53lem.3	. . . . 5 c2 a0 a1 b0 b1
6		dp53lem.4	. . . . 5 p0 a1 b1 a2 b2
7		dp53lem.5	. . . . 5 a0 b0 a1 b1 a2 b2
8	3, 4, 5, 6, 7	dp53lema 1161	. . . 4 b1 b0 a0 p0 b1 a0 a1 c0 c1
9	2, 8	letr 137	. . 3 b0 a0 p0 b1 a0 a1 c0 c1
10	1, 9	ler2an 173	. 2 b0 a0 p0 b0 b1 a0 a1 c0 c1
11	3, 4, 5, 6, 7	dp53lemc 1163	. . . 4 b0 a0 b0 b1 c2 c0 c1 b0 b1 c2 c0 c1
12	3, 4, 5, 6, 7	dp53lemb 1162	. . . 4 b0 b1 c2 c0 c1 b0 b1 a0 a1 c0 c1
13	11, 12	tr 62	. . 3 b0 a0 b0 b1 c2 c0 c1 b0 b1 a0 a1 c0 c1
14	13	cm 61	. 2 b0 b1 a0 a1 c0 c1 b0 a0 b0 b1 c2 c0 c1
15	10, 14	lbtr 139	1 b0 a0 p0 b0 a0 b0 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:  dp53leme  1165

Copyright terms: Public domain

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