Definition df-qs 7748

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 ) = { 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 7741	. 2 class ( A /. R )
4		vy	. . . . . 6 setvar y
5	4	cv 1482	. . . . 5 class y
6		vx	. . . . . . 7 setvar x
7	6	cv 1482	. . . . . 6 class x
8	7, 2	cec 7740	. . . . 5 class [ x ] R
9	5, 8	wceq 1483	. . . 4 wff y = [ x ] R
10	9, 6, 1	wrex 2913	. . 3 wff E. x e. A y = [ x ] R
11	10, 4	cab 2608	. 2 class { y | E. x e. A y = [ x ] R }
12	3, 11	wceq 1483	1 wff ( A /. R ) = { y | E. x e. A y = [ x ] R }

This definition is referenced by:  qseq1  7796  qseq2  7797  elqsg  7798  qsexg  7805  uniqs  7807  snec  7810  qsinxp  7823  qliftf  7835  quslem  16203  pi1xfrf  22853  pi1cof  22859  qsss1  34053  qsresid  34096  uniqsALTV  34101  0qs  34133