Definition df-ec 3202

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. The Definition of [Enderton] p. 57 uses the notation [A] (subscript) R, although we simply follow the brackets by R since we don't have subscripts. For an alternate definition, see ec2 3203.

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 3198	. 2 class [A]R
4	1	csn 1808	. . 3 class {A}
5	2, 4	cima 2413	. 2 class (R “ {A})
6	3, 5	wceq 1091	1 wff [A]R = (R “ {A})

This definition is referenced by:  ec2 3203  ecexg 3204  eceq1 3214  eceq2 3215  ecidsn 3224

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