Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-ec Structured version   Unicode version

Definition df-ec 6910
 Description: Define the -coset of . Exercise 35 of [Enderton] p. 61. This is called the equivalence class of modulo when is an equivalence relation (i.e. when ; see dfer2 6909). In this case, is a representative (member) of the equivalence class , which contains all sets that are equivalent to . Definition of [Enderton] p. 57 uses the notation (subscript) , although we simply follow the brackets by since we don't have subscripted expressions. For an alternate definition, see dfec2 6911. (Contributed by NM, 23-Jul-1995.)
Assertion
Ref Expression
df-ec

Detailed syntax breakdown of Definition df-ec
StepHypRef Expression
1 cA . . 3
2 cR . . 3
31, 2cec 6906 . 2
41csn 3816 . . 3
52, 4cima 4884 . 2
63, 5wceq 1653 1
 Colors of variables: wff set class This definition is referenced by:  dfec2  6911  ecexg  6912  ecexr  6913  eceq1  6944  eceq2  6945  elecg  6946  ecss  6949  ecidsn  6956  uniqs  6967  ecqs  6971  ecinxp  6982
 Copyright terms: Public domain W3C validator