Definition df-qus 12889

Description: Define a quotient ring (or quotient group), which is a special case of an image structure df-iimas 12888 where the image function is 𝑥 ↦ [𝑥]𝑒. (Contributed by Mario Carneiro, 23-Feb-2015.)

Assertion

Ref	Expression
df-qus	⊢ /s = (𝑟 ∈ V, 𝑒 ∈ V ↦ ((𝑥 ∈ (Base‘𝑟) ↦ [𝑥]𝑒) “s 𝑟))

Distinct variable group:   𝑒,𝑟,𝑥

Detailed syntax breakdown of Definition df-qus

Step	Hyp	Ref	Expression
1		cqus 12886	. 2 class /s
2		vr	. . 3 setvar 𝑟
3		ve	. . 3 setvar 𝑒
4		cvv 2760	. . 3 class V
5		vx	. . . . 5 setvar 𝑥
6	2	cv 1363	. . . . . 6 class 𝑟
7		cbs 12621	. . . . . 6 class Base
8	6, 7	cfv 5255	. . . . 5 class (Base‘𝑟)
9	5	cv 1363	. . . . . 6 class 𝑥
10	3	cv 1363	. . . . . 6 class 𝑒
11	9, 10	cec 6587	. . . . 5 class [𝑥]𝑒
12	5, 8, 11	cmpt 4091	. . . 4 class (𝑥 ∈ (Base‘𝑟) ↦ [𝑥]𝑒)
13		cimas 12885	. . . 4 class “s
14	12, 6, 13	co 5919	. . 3 class ((𝑥 ∈ (Base‘𝑟) ↦ [𝑥]𝑒) “s 𝑟)
15	2, 3, 4, 4, 14	cmpo 5921	. 2 class (𝑟 ∈ V, 𝑒 ∈ V ↦ ((𝑥 ∈ (Base‘𝑟) ↦ [𝑥]𝑒) “s 𝑟))
16	1, 15	wceq 1364	1 wff /s = (𝑟 ∈ V, 𝑒 ∈ V ↦ ((𝑥 ∈ (Base‘𝑟) ↦ [𝑥]𝑒) “s 𝑟))

This definition is referenced by:  qusval  12909  qusex  12911