Definition df-qus 13135

Description: Define a quotient ring (or quotient group), which is a special case of an image structure df-iimas 13134 where the image function is x |-> [ x ] e. (Contributed by Mario Carneiro, 23-Feb-2015.)

Assertion

Ref	Expression
df-qus	|- /.s = ( r e. _V , e e. _V |-> ( ( x e. ( Base ` r ) |-> [ x ] e ) "s r ) )

Distinct variable group:   e, r, x

Detailed syntax breakdown of Definition df-qus

Step	Hyp	Ref	Expression
1		cqus 13132	. 2 class /.s
2		vr	. . 3 setvar r
3		ve	. . 3 setvar e
4		cvv 2772	. . 3 class _V
5		vx	. . . . 5 setvar x
6	2	cv 1372	. . . . . 6 class r
7		cbs 12832	. . . . . 6 class Base
8	6, 7	cfv 5271	. . . . 5 class ( Base ` r )
9	5	cv 1372	. . . . . 6 class x
10	3	cv 1372	. . . . . 6 class e
11	9, 10	cec 6618	. . . . 5 class [ x ] e
12	5, 8, 11	cmpt 4105	. . . 4 class ( x e. ( Base ` r ) |-> [ x ] e )
13		cimas 13131	. . . 4 class "s
14	12, 6, 13	co 5944	. . 3 class ( ( x e. ( Base ` r ) |-> [ x ] e ) "s r )
15	2, 3, 4, 4, 14	cmpo 5946	. 2 class ( r e. _V , e e. _V |-> ( ( x e. ( Base ` r ) |-> [ x ] e ) "s r ) )
16	1, 15	wceq 1373	1 wff /.s = ( r e. _V , e e. _V |-> ( ( x e. ( Base ` r ) |-> [ x ] e ) "s r ) )

This definition is referenced by:  qusval  13155  qusex  13157