Definition df-qs 5524

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

Assertion

Ref	Expression
df-qs	|- (A/.R) = {y | E.x e. 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 5518	. 2 class (A/.R)
4		vy	. . . . . 6 set y
5	4	cv 1614	. . . . 5 class y
6		vx	. . . . . . 7 set x
7	6	cv 1614	. . . . . 6 class x
8	7, 2	cec 5517	. . . . 5 class [x]R
9	5, 8	wceq 1615	. . . 4 wff y = [x]R
10	9, 6, 1	wrex 2386	. . 3 wff E.x e. A y = [x]R
11	10, 4	cab 2157	. 2 class {y | E.x e. A y = [x]R}
12	3, 11	wceq 1615	1 wff (A/.R) = {y | E.x e. A y = [x]R}

This definition is referenced by:  qseq1 5550  qseq2 5551  elqs 5552  qsexg 5556  snec 5559  qsid 5564  eroprlem 16817  eropreu 16818  elqs2 17352

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