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Definition df-dif 3312
Description: Define class difference, also called relative complement. Definition 5.12 of [TakeutiZaring] p. 20. For example, ?Error: 1 , 3 } \ { 1 , 8 } ) = { 3 } ^ This math symbol is not active (i.e. was not declared in this scope). ({1,3}\{1,8})={3} (ex-dif 21782). Contrast this operation with union (df-un 3314) and intersection (df-in 3316). 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 3306 . 2
4 vx . . . . . 6
54cv 1653 . . . . 5
65, 1wcel 1728 . . . 4
75, 2wcel 1728 . . . . 5
87wn 3 . . . 4
96, 8wa 360 . . 3
109, 4cab 2429 . 2
113, 10wceq 1654 1
Colors of variables: wff set class
This definition is referenced by:  dfdif2  3318  eldif  3319
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