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Definition df-qs 6662
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 6655 . 2  class  ( A /. R )
4 vy . . . . . 6  set  y
54cv 1622 . . . . 5  class  y
6 vx . . . . . . 7  set  x
76cv 1622 . . . . . 6  class  x
87, 2cec 6654 . . . . 5  class  [ x ] R
95, 8wceq 1623 . . . 4  wff  y  =  [ x ] R
109, 6, 1wrex 2545 . . 3  wff  E. x  e.  A  y  =  [ x ] R
1110, 4cab 2270 . 2  class  { y  |  E. x  e.  A  y  =  [
x ] R }
123, 11wceq 1623 1  wff  ( A /. R )  =  { y  |  E. x  e.  A  y  =  [ x ] R }
Colors of variables: wff set class
This definition is referenced by:  qseq1  6705  qseq2  6706  elqsg  6707  qsexg  6713  uniqs  6715  snec  6718  qsinxp  6731  qliftf  6742  divslem  13441  pi1xfrf  18547  pi1cof  18553
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