Definition df-ec 6813

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 6812). 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 6814. (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 6809	. 2 class [ A ] R
4	1	csn 3709	. . 3 class { A }
5	2, 4	cima 4779	. 2 class ( R " { A } )
6	3, 5	wceq 1402	1 wff [ A ] R = ( R " { A } )

This definition is used by:  dfec2  6814  ecexg  6815  ecexr  6816  eceq1  6846  eceq2  6848  elecg  6851  ecss  6854  ecidsn  6860  uniqs  6871  ecqs  6875  ecinxp  6888