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Definition df-ec 6015
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 6014). 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 6016. (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 6011 . 2 class [A]𝑅
41csn 3346 . . 3 class {A}
52, 4cima 4271 . 2 class (𝑅 “ {A})
63, 5wceq 1226 1 wff [A]𝑅 = (𝑅 “ {A})
Colors of variables: wff set class
This definition is referenced by:  dfec2  6016  ecexg  6017  ecexr  6018  eceq1  6048  eceq2  6050  elecg  6051  ecss  6054  ecidsn  6060  uniqs  6071  ecqs  6075  ecinxp  6088
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