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Definition df-ec 6438
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 6437). 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 6439. (Contributed by NM, 23-Jul-1995.)
Assertion
Ref Expression
df-ec  |-  [ A ] R  =  ( R " { A }
)

Detailed syntax breakdown of Definition df-ec
StepHypRef Expression
1 cA . . 3  class  A
2 cR . . 3  class  R
31, 2cec 6434 . 2  class  [ A ] R
41csn 3531 . . 3  class  { A }
52, 4cima 4549 . 2  class  ( R
" { A }
)
63, 5wceq 1332 1  wff  [ A ] R  =  ( R " { A }
)
Colors of variables: wff set class
This definition is referenced by:  dfec2  6439  ecexg  6440  ecexr  6441  eceq1  6471  eceq2  6473  elecg  6474  ecss  6477  ecidsn  6483  uniqs  6494  ecqs  6498  ecinxp  6511
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