Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  df-dif Unicode version

Definition df-dif 3155
 Description: Define class difference, also called relative complement. Definition 5.12 of [TakeutiZaring] p. 20. For example, (ex-dif 20810). Contrast this operation with union (df-un 3157) and intersection (df-in 3159). 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 3149 . 2
4 vx . . . . . 6
54cv 1622 . . . . 5
65, 1wcel 1684 . . . 4
75, 2wcel 1684 . . . . 5
87wn 3 . . . 4
96, 8wa 358 . . 3
109, 4cab 2269 . 2
113, 10wceq 1623 1
 Colors of variables: wff set class This definition is referenced by:  dfdif2  3161  eldif  3162  ballotth  23096
 Copyright terms: Public domain W3C validator