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Definition df-qs 6903
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 6896 . 2  class  ( A /. R )
4 vy . . . . . 6  set  y
54cv 1651 . . . . 5  class  y
6 vx . . . . . . 7  set  x
76cv 1651 . . . . . 6  class  x
87, 2cec 6895 . . . . 5  class  [ x ] R
95, 8wceq 1652 . . . 4  wff  y  =  [ x ] R
109, 6, 1wrex 2698 . . 3  wff  E. x  e.  A  y  =  [ x ] R
1110, 4cab 2421 . 2  class  { y  |  E. x  e.  A  y  =  [
x ] R }
123, 11wceq 1652 1  wff  ( A /. R )  =  { y  |  E. x  e.  A  y  =  [ x ] R }
Colors of variables: wff set class
This definition is referenced by:  qseq1  6946  qseq2  6947  elqsg  6948  qsexg  6954  uniqs  6956  snec  6959  qsinxp  6972  qliftf  6984  divslem  13760  pi1xfrf  19070  pi1cof  19076
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