Definition df-ec 6809

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 6808). 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 6810. (Contributed by NM, 23-Jul-1995.)

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 6805	. 2 class [ A ] R
4	1	csn 3709	. . 3 class { A }
5	2, 4	cima 4777	. 2 class ( R " { A } )
6	3, 5	wceq 1402	1 wff [ A ] R = ( R " { A } )

This definition is used by:  dfec2  6810  ecexg  6811  ecexr  6812  eceq1  6842  eceq2  6844  elecg  6847  ecss  6850  ecidsn  6856  uniqs  6867  ecqs  6871  ecinxp  6884