Definition df-qs 4256

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 4250	. 2 class (A/.R)
4		vy	. . . . . 6 set y
5	4	cv 953	. . . . 5 class y
6		vx	. . . . . . 7 set x
7	6	cv 953	. . . . . 6 class x
8	7, 2	cec 4249	. . . . 5 class [x]R
9	5, 8	wceq 954	. . . 4 wff y = [x]R
10	9, 6, 1	wrex 1643	. . 3 wff E.x e. A y = [x]R
11	10, 4	cab 1461	. 2 class {y | E.x e. A y = [x]R}
12	3, 11	wceq 954	1 wff (A/.R) = {y | E.x e. A y = [x]R}

This definition is referenced by:  qseq1 4278  qseq2 4279  elqs 4280  qsexg 4284  snec 4286  qsid 4291

Copyright terms: Public domain