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Definition df-qus 16371
Description: Define a quotient ring (or quotient group), which is a special case of an image structure df-imas 16370 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
StepHypRef Expression
1 cqus 16367 . 2 class /s
2 vr . . 3 setvar 𝑟
3 ve . . 3 setvar 𝑒
4 cvv 3340 . . 3 class V
5 vx . . . . 5 setvar 𝑥
62cv 1631 . . . . . 6 class 𝑟
7 cbs 16059 . . . . . 6 class Base
86, 7cfv 6049 . . . . 5 class (Base‘𝑟)
95cv 1631 . . . . . 6 class 𝑥
103cv 1631 . . . . . 6 class 𝑒
119, 10cec 7909 . . . . 5 class [𝑥]𝑒
125, 8, 11cmpt 4881 . . . 4 class (𝑥 ∈ (Base‘𝑟) ↦ [𝑥]𝑒)
13 cimas 16366 . . . 4 class s
1412, 6, 13co 6813 . . 3 class ((𝑥 ∈ (Base‘𝑟) ↦ [𝑥]𝑒) “s 𝑟)
152, 3, 4, 4, 14cmpt2 6815 . 2 class (𝑟 ∈ V, 𝑒 ∈ V ↦ ((𝑥 ∈ (Base‘𝑟) ↦ [𝑥]𝑒) “s 𝑟))
161, 15wceq 1632 1 wff /s = (𝑟 ∈ V, 𝑒 ∈ V ↦ ((𝑥 ∈ (Base‘𝑟) ↦ [𝑥]𝑒) “s 𝑟))
Colors of variables: wff setvar class
This definition is referenced by:  qusval  16404
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