Definition df-divs 14565

Description: Define a quotient ring (or quotient group), which is a special case of an image structure df-imas 14564 where the image function is x |-> [ x ] e. (Contributed by Mario Carneiro, 23-Feb-2015.)

Assertion

Ref	Expression
df-divs	|- /.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-divs

Step	Hyp	Ref	Expression
1		cqus 14561	. 2 class /.s
2		vr	. . 3 setvar r
3		ve	. . 3 setvar e
4		cvv 3076	. . 3 class _V
5		vx	. . . . 5 setvar x
6	2	cv 1369	. . . . . 6 class r
7		cbs 14291	. . . . . 6 class Base
8	6, 7	cfv 5525	. . . . 5 class ( Base ` r )
9	5	cv 1369	. . . . . 6 class x
10	3	cv 1369	. . . . . 6 class e
11	9, 10	cec 7208	. . . . 5 class [ x ] e
12	5, 8, 11	cmpt 4457	. . . 4 class ( x e. ( Base ` r ) |-> [ x ] e )
13		cimas 14560	. . . 4 class "s
14	12, 6, 13	co 6199	. . 3 class ( ( x e. ( Base ` r ) |-> [ x ] e ) "s r )
15	2, 3, 4, 4, 14	cmpt2 6201	. 2 class ( r e. _V , e e. _V |-> ( ( x e. ( Base ` r ) |-> [ x ] e ) "s r ) )
16	1, 15	wceq 1370	1 wff /.s = ( r e. _V , e e. _V |-> ( ( x e. ( Base ` r ) |-> [ x ] e ) "s r ) )

This definition is referenced by:  divsval  14598