Definition df-ec 6503

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 6502). 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 6504. (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 6499	. 2 class [ A ] R
4	1	csn 3576	. . 3 class { A }
5	2, 4	cima 4607	. 2 class ( R " { A } )
6	3, 5	wceq 1343	1 wff [ A ] R = ( R " { A } )

This definition is referenced by:  dfec2  6504  ecexg  6505  ecexr  6506  eceq1  6536  eceq2  6538  elecg  6539  ecss  6542  ecidsn  6548  uniqs  6559  ecqs  6563  ecinxp  6576