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Definition df-ec 6044
Description: Define the  R-coset of . Exercise 35 of [Enderton] p. 61. This is called the equivalence class of modulo  R when  R is an equivalence relation (i.e. when  Er  R; see dfer2 6043). In this case, is a representative (member) of the equivalence class  R, which contains all sets that are equivalent to . Definition of [Enderton] p. 57 uses the notation (subscript)  R, although we simply follow the brackets by  R since we don't have subscripted expressions. For an alternate definition, see dfec2 6045. (Contributed by NM, 23-Jul-1995.)
Assertion
Ref Expression
df-ec  R  R " { }

Detailed syntax breakdown of Definition df-ec
StepHypRef Expression
1 cA . . 3
2 cR . . 3  R
31, 2cec 6040 . 2  R
41csn 3367 . . 3  { }
52, 4cima 4291 . 2  R
" { }
63, 5wceq 1242 1  R  R " { }
Colors of variables: wff set class
This definition is referenced by:  dfec2  6045  ecexg  6046  ecexr  6047  eceq1  6077  eceq2  6079  elecg  6080  ecss  6083  ecidsn  6089  uniqs  6100  ecqs  6104  ecinxp  6117
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