Definition df-ec

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

	Ref	Expression
Assertion	df-ec	$$⊢\left[A\right]R=R\left[\left\{A\right\}\right]$$

Detailed syntax breakdown

Step	Hyp	Ref	Expression
0		cA	$$classA$$
1		cR	$$classR$$
2	0 1	cec	$$class\left[A\right]R$$
3	0	csn	$$class\left\{A\right\}$$
4	1 3	cima	$$classR\left[\left\{A\right\}\right]$$
5	2 4	wceq	$$wff\left[A\right]R=R\left[\left\{A\right\}\right]$$