Definition df-qs 5952

Description: Define quotient set. R is usually an equivalence relation. Definition of [Enderton] p. 58. (Contributed by set.mm contributors, 22-Feb-2015.)

Assertion

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

Distinct variable groups:   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 5947	. 2 class (A / R)
4		vy	. . . . . 6 setvar y
5	4	cv 1641	. . . . 5 class y
6		vx	. . . . . . 7 setvar x
7	6	cv 1641	. . . . . 6 class x
8	7, 2	cec 5946	. . . . 5 class [x]R
9	5, 8	wceq 1642	. . . 4 wff y = [x]R
10	9, 6, 1	wrex 2616	. . 3 wff ∃x ∈ A y = [x]R
11	10, 4	cab 2339	. 2 class {y ∣ ∃x ∈ A y = [x]R}
12	3, 11	wceq 1642	1 wff (A / R) = {y ∣ ∃x ∈ A y = [x]R}

This definition is referenced by:  qseq1  5975  qseq2  5976  elqsg  5977  qsexg  5983  uniqs  5985  snec  5988