Definition df-ec 7744

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 7743). 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 7745. (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 7740	. 2 class [ A ] R
4	1	csn 4177	. . 3 class { A }
5	2, 4	cima 5117	. 2 class ( R " { A } )
6	3, 5	wceq 1483	1 wff [ A ] R = ( R " { A } )

This definition is referenced by:  dfec2  7745  ecexg  7746  ecexr  7747  eceq1  7782  eceq2  7784  elecg  7785  ecss  7788  ecidsn  7795  uniqs  7807  ecqs  7811  ecinxp  7822  elecALTV  34030  uniqsALTV  34101  ec0  34132