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Definition df-ec 7099
Description: Define the  R-coset of  A. Exercise 35 of [Enderton] p. 61. This is called the equivalence class of  A modulo  R when  R is an equivalence relation (i.e. when  Er  R; see dfer2 7098). In this case,  A is a representative (member) of the equivalence class  [ A ] R, which contains all sets that are equivalent to  A. Definition of [Enderton] p. 57 uses the notation  [ A ] (subscript)  R, although we simply follow the brackets by  R since we don't have subscripted expressions. For an alternate definition, see dfec2 7100. (Contributed by NM, 23-Jul-1995.)
Assertion
Ref Expression
df-ec  |-  [ A ] R  =  ( R " { A }
)

Detailed syntax breakdown of Definition df-ec
StepHypRef Expression
1 cA . . 3  class  A
2 cR . . 3  class  R
31, 2cec 7095 . 2  class  [ A ] R
41csn 3874 . . 3  class  { A }
52, 4cima 4839 . 2  class  ( R
" { A }
)
63, 5wceq 1364 1  wff  [ A ] R  =  ( R " { A }
)
Colors of variables: wff setvar class
This definition is referenced by:  dfec2  7100  ecexg  7101  ecexr  7102  eceq1  7133  eceq2  7134  elecg  7135  ecss  7138  ecidsn  7145  uniqs  7156  ecqs  7160  ecinxp  7171
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