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	⊢ 𝐴
1		cR	⊢ 𝑅
2	0 1	cec	⊢ [ 𝐴 ] 𝑅
3	0	csn	⊢ { 𝐴 }
4	1 3	cima	⊢ ( 𝑅 “ { 𝐴 } )
5	2 4	wceq	⊢ [ 𝐴 ] 𝑅 = ( 𝑅 “ { 𝐴 } )