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Definition df-qs 6552
Description: Define quotient set.  R is usually an equivalence relation. Definition of [Enderton] p. 58. (Contributed by NM, 23-Jul-1995.)
Assertion
Ref Expression
df-qs  |-  ( A /. R )  =  { y  |  E. x  e.  A  y  =  [ x ] R }
Distinct variable groups:    x, y, A    x, R, y

Detailed syntax breakdown of Definition df-qs
StepHypRef Expression
1 cA . . 3  class  A
2 cR . . 3  class  R
31, 2cqs 6545 . 2  class  ( A /. R )
4 vy . . . . . 6  set  y
54cv 1618 . . . . 5  class  y
6 vx . . . . . . 7  set  x
76cv 1618 . . . . . 6  class  x
87, 2cec 6544 . . . . 5  class  [ x ] R
95, 8wceq 1619 . . . 4  wff  y  =  [ x ] R
109, 6, 1wrex 2510 . . 3  wff  E. x  e.  A  y  =  [ x ] R
1110, 4cab 2239 . 2  class  { y  |  E. x  e.  A  y  =  [
x ] R }
123, 11wceq 1619 1  wff  ( A /. R )  =  { y  |  E. x  e.  A  y  =  [ x ] R }
Colors of variables: wff set class
This definition is referenced by:  qseq1  6595  qseq2  6596  elqsg  6597  qsexg  6603  uniqs  6605  snec  6608  qsinxp  6621  qliftf  6632  divslem  13319  pi1xfrf  18383  pi1cof  18389
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