Definition df-ec 4263

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. The Definition of [Enderton] p. 57 uses the notation [A] (subscript) R, although we simply follow the brackets by R since we don't have subscripts. For an alternate definition, see dfec2 4264.

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 4259	. 2 class [A]R
4	1	csn 2409	. . 3 class {A}
5	2, 4	cima 3173	. 2 class (R"{A})
6	3, 5	wceq 956	1 wff [A]R = (R"{A})

This definition is referenced by:  dfec2 4264  ecexg 4265  eceq1 4277  eceq2 4278  ecidsn 4287

Copyright terms: Public domain