Metamath Proof Explorer

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 A R = R A

Detailed syntax breakdown

Step Hyp Ref Expression
0 cA class A
1 cR class R
2 0 1 cec class A R
3 0 csn class A
4 1 3 cima class R A
5 2 4 wceq wff A R = R A