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Definition df-qs 6048
Description: Define quotient set. 𝑅 is usually an equivalence relation. Definition of [Enderton] p. 58. (Contributed by NM, 23-Jul-1995.)
Assertion
Ref Expression
df-qs (A / 𝑅) = {yx A y = [x]𝑅}
Distinct variable groups:   x,y,A   x,𝑅,y

Detailed syntax breakdown of Definition df-qs
StepHypRef Expression
1 cA . . 3 class A
2 cR . . 3 class 𝑅
31, 2cqs 6041 . 2 class (A / 𝑅)
4 vy . . . . . 6 setvar y
54cv 1241 . . . . 5 class y
6 vx . . . . . . 7 setvar x
76cv 1241 . . . . . 6 class x
87, 2cec 6040 . . . . 5 class [x]𝑅
95, 8wceq 1242 . . . 4 wff y = [x]𝑅
109, 6, 1wrex 2301 . . 3 wff x A y = [x]𝑅
1110, 4cab 2023 . 2 class {yx A y = [x]𝑅}
123, 11wceq 1242 1 wff (A / 𝑅) = {yx A y = [x]𝑅}
Colors of variables: wff set class
This definition is referenced by:  qseq1  6090  qseq2  6091  elqsg  6092  qsexg  6098  uniqs  6100  snec  6103  qsinxp  6118  qliftf  6127
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