Quantum Logic Explorer		< Previous   Next > Nearby theorems
Mirrors  >  Home  >  QLE Home  >  Th. List  >  dp53lemc		Unicode version

---

Theorem dp53lemc 1163

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
dp53lemc	b0 a0 b0 b1 c2 c0 c1 b0 b1 c2 c0 c1

---

Proof of Theorem dp53lemc

Step	Hyp	Ref	Expression
1		or32 82	. . 3 a0 b0 b1 c2 c0 c1 a0 b0 c2 c0 c1 b1
2		orcom 73	. . 3 a0 b0 c2 c0 c1 b1 b1 a0 b0 c2 c0 c1
3		leo 158	. . . . . . . 8 a0 a0 a1
4		leo 158	. . . . . . . 8 b0 b0 b1
5	3, 4	le2an 169	. . . . . . 7 a0 b0 a0 a1 b0 b1
6		dp53lem.3	. . . . . . . 8 c2 a0 a1 b0 b1
7	6	cm 61	. . . . . . 7 a0 a1 b0 b1 c2
8	5, 7	lbtr 139	. . . . . 6 a0 b0 c2
9		leo 158	. . . . . . . . 9 a0 a0 a2
10		leo 158	. . . . . . . . 9 b0 b0 b2
11	9, 10	le2an 169	. . . . . . . 8 a0 b0 a0 a2 b0 b2
12		dp53lem.2	. . . . . . . . 9 c1 a0 a2 b0 b2
13	12	cm 61	. . . . . . . 8 a0 a2 b0 b2 c1
14	11, 13	lbtr 139	. . . . . . 7 a0 b0 c1
15	14	lerr 150	. . . . . 6 a0 b0 c0 c1
16	8, 15	ler2an 173	. . . . 5 a0 b0 c2 c0 c1
17	16	df-le2 131	. . . 4 a0 b0 c2 c0 c1 c2 c0 c1
18	17	lor 70	. . 3 b1 a0 b0 c2 c0 c1 b1 c2 c0 c1
19	1, 2, 18	3tr 65	. 2 a0 b0 b1 c2 c0 c1 b1 c2 c0 c1
20	19	lan 77	1 b0 a0 b0 b1 c2 c0 c1 b0 b1 c2 c0 c1

Colors of variables: term

Syntax hints:   wb 1   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

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:  dp53lemd  1164

Copyright terms: Public domain

W3C validator