df-edring - Mathbox for Norm Megill

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Definition df-edring 34287

Description: Define division ring on trace-preserving endomorphisms. The multiplication operation is reversed composition, per the definition of E of [Crawley] p. 117, 4th line from bottom. (Contributed by NM, 8-Jun-2013.)

**Assertion**
Ref	Expression
df-edring

Distinct variable group:

**Detailed syntax breakdown of Definition df-edring**
Step	Hyp	Ref	Expression
1		cedring 34283	. 2
2		vk	. . 3
3		cvv 3082	. . 3
4		vw	. . . 4
5	2	cv 1437	. . . . 5
6		clh 33512	. . . . 5
7	5, 6	cfv 5599	. . . 4
8		cnx 15111	. . . . . . 7
9		cbs 15114	. . . . . . 7
10	8, 9	cfv 5599	. . . . . 6
11	4	cv 1437	. . . . . . 7
12		ctendo 34282	. . . . . . . 8
13	5, 12	cfv 5599	. . . . . . 7
14	11, 13	cfv 5599	. . . . . 6
15	10, 14	cop 4003	. . . . 5
16		cplusg 15183	. . . . . . 7
17	8, 16	cfv 5599	. . . . . 6
18		vs	. . . . . . 7
19		vt	. . . . . . 7
20		vf	. . . . . . . 8
21		cltrn 33629	. . . . . . . . . 10
22	5, 21	cfv 5599	. . . . . . . . 9
23	11, 22	cfv 5599	. . . . . . . 8
24	20	cv 1437	. . . . . . . . . 10
25	18	cv 1437	. . . . . . . . . 10
26	24, 25	cfv 5599	. . . . . . . . 9
27	19	cv 1437	. . . . . . . . . 10
28	24, 27	cfv 5599	. . . . . . . . 9
29	26, 28	ccom 4855	. . . . . . . 8
30	20, 23, 29	cmpt 4480	. . . . . . 7
31	18, 19, 14, 14, 30	cmpt2 6305	. . . . . 6
32	17, 31	cop 4003	. . . . 5
33		cmulr 15184	. . . . . . 7
34	8, 33	cfv 5599	. . . . . 6
35	25, 27	ccom 4855	. . . . . . 7
36	18, 19, 14, 14, 35	cmpt2 6305	. . . . . 6
37	34, 36	cop 4003	. . . . 5
38	15, 32, 37	ctp 4001	. . . 4
39	4, 7, 38	cmpt 4480	. . 3
40	2, 3, 39	cmpt 4480	. 2
41	1, 40	wceq 1438	1

Colors of variables: wff setvar class

This definition is referenced by: erngfset 34329

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