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Definition df-divs 13412
Description: Define a quotient ring (or quotient group), which is a special case of an image structure df-imas 13411 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
StepHypRef Expression
1 cqus 13408 . 2  class  /.s
2 vr . . 3  set  r
3 ve . . 3  set  e
4 cvv 2788 . . 3  class  _V
5 vx . . . . 5  set  x
62cv 1622 . . . . . 6  class  r
7 cbs 13148 . . . . . 6  class  Base
86, 7cfv 5255 . . . . 5  class  ( Base `  r )
95cv 1622 . . . . . 6  class  x
103cv 1622 . . . . . 6  class  e
119, 10cec 6658 . . . . 5  class  [ x ] e
125, 8, 11cmpt 4077 . . . 4  class  ( x  e.  ( Base `  r
)  |->  [ x ]
e )
13 cimas 13407 . . . 4  class  "s
1412, 6, 13co 5858 . . 3  class  ( ( x  e.  ( Base `  r )  |->  [ x ] e )  "s  r
)
152, 3, 4, 4, 14cmpt2 5860 . 2  class  ( r  e.  _V ,  e  e.  _V  |->  ( ( x  e.  ( Base `  r )  |->  [ x ] e )  "s  r
) )
161, 15wceq 1623 1  wff  /.s  =  (
r  e.  _V , 
e  e.  _V  |->  ( ( x  e.  (
Base `  r )  |->  [ x ] e )  "s  r ) )
Colors of variables: wff set class
This definition is referenced by:  divsval  13444
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