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Definition df-ec 7332
Description: Define the -coset of . Exercise 35 of [Enderton] p. 61. This is called the equivalence class of modulo when is an equivalence relation (i.e. when Er ; see dfer2 7331). In this case, is a representative (member) of the equivalence class , which contains all sets that are equivalent to . Definition of [Enderton] p. 57 uses the notation [A] (subscript) , although we simply follow the brackets by since we don't have subscripted expressions. For an alternate definition, see dfec2 7333. (Contributed by NM, 23-Jul-1995.)
Assertion
Ref Expression
df-ec

Detailed syntax breakdown of Definition df-ec
StepHypRef Expression
1 cA . . 3
2 cR . . 3
31, 2cec 7328 . 2
41csn 4029 . . 3
52, 4cima 5007 . 2
63, 5wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  dfec2  7333  ecexg  7334  ecexr  7335  eceq1  7366  eceq2  7368  elecg  7369  ecss  7372  ecidsn  7379  uniqs  7390  ecqs  7394  ecinxp  7405
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