Definition df-qs 3205

Description: Define quotient set. R is usually an equivalence relation. Definition of [Enderton] p. 58.

Assertion

Ref	Expression
df-qs	⊢ (A / R) = {y∣∃x ∈ A y = [x]R}

Distinct variable group(s):   x,y,A   x,R,y

Detailed syntax breakdown of Definition df-qs

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cR	. . 3 class R
3	1, 2	cqs 3199	. 2 class (A / R)
4		vy	. . . . . 6 set y
5	4	cv 1089	. . . . 5 class y
6		vx	. . . . . . 7 set x
7	6	cv 1089	. . . . . 6 class x
8	7, 2	cec 3198	. . . . 5 class [x]R
9	5, 8	wceq 1091	. . . 4 wff y = [x]R
10	9, 6, 1	wrex 1202	. . 3 wff ∃x ∈ A y = [x]R
11	10, 4	cab 1090	. 2 class {y∣∃x ∈ A y = [x]R}
12	3, 11	wceq 1091	1 wff (A / R) = {y∣∃x ∈ A y = [x]R}

This definition is referenced by:  qseq1 3225  qseq2 3226  elqs 3227  qsex 3231  snec 3232  qsid 3237

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