Definition df-ec 5948

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. 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 5949. (Contributed by set.mm contributors, 22-Feb-2015.)

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 5946	. 2 class [A]R
4	1	csn 3738	. . 3 class {A}
5	2, 4	cima 4723	. 2 class (R"{A})
6	3, 5	wceq 1642	1 wff [A]R = (R"{A})

This definition is referenced by:  dfec2  5949  ecexg  5950  ecexr  5951  eceq1  5963  eceq2  5964  elec  5965  ecss  5967  ecidsn  5974  uniqs  5985  ecqs  5989  ecid  5990