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Definition df-dif 2893
Description: Define class difference, also called relative complement. Definition 5.12 of [TakeutiZaring] p. 20. Contrast this operation with union  u. (df-un 2895) and intersection  i^i (df-in 2897). Several notations are used in the literature; we chose the  \ convention used in Definition 5.3 of [Eisenberg] p. 67 instead of the more common minus sign to reserve the latter for later use in, e.g., arithmetic. We will use the terminology " excludes " to mean  \ . We will use " is removed from " to mean  \  { } i.e. the removal of an element or equivalently the exclusion of a singleton. (Contributed by NM, 29-Apr-1994.)
Assertion
Ref Expression
df-dif 
\  {  |  }
Distinct variable groups:   ,   ,

Detailed syntax breakdown of Definition df-dif
StepHypRef Expression
1 cA . . 3
2 cB . . 3
31, 2cdif 2887 . 2 
\
4 vx . . . . . 6  setvar
54cv 1225 . . . . 5
65, 1wcel 1370 . . . 4
75, 2wcel 1370 . . . . 5
87wn 3 . . . 4
96, 8wa 97 . . 3
109, 4cab 2004 . 2  {  |  }
113, 10wceq 1226 1  \  {  |  }
Colors of variables: wff set class
This definition is referenced by:  dfdif2  2899  eldif  2900  bdcdif  7280
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