Definition df-ec 5320

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 5319). 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 5321.

Assertion

Ref	Expression
df-ec	|- [A]R = (R"{A})

Detailed syntax breakdown of Definition df-ec

Step	Hyp	Ref	Expression
1		cA	. . 3 class A
2		cR	. . 3 class R
3	1, 2	cec 5316	. 2 class [A]R
4	1	csn 3044	. . 3 class {A}
5	2, 4	cima 3989	. 2 class (R"{A})
6	3, 5	wceq 1298	1 wff [A]R = (R"{A})

This definition is referenced by:  dfec2 5321  ecexg 5322  eceq1 5335  eceq2 5336  ecidsn 5345  ecqs 5356

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