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

Definition df-supp 6919
Description: Define the support of a function against a "zero" value. According to Wikipedia ("Support (mathematics)", 31-Mar-2019, https://en.wikipedia.org/wiki/Support_(mathematics)) "In mathematics, the support of a real-valued function f is the subset of the domain containing those elements which are not mapped to zero." and "The notion of support also extends in a natural way to functions taking values in more general sets than R [the real numbers] and to other objects.". The following definition allows for such extensions, being applicable for any sets (which usually are functions) and any element (even not necessarily from the range of the function) regarded as "zero". (Contributed by AV, 31-Mar-2019.) (Revised by AV, 6-Apr-2019.)
Assertion
Ref Expression
df-supp
Distinct variable group:   , ,

Detailed syntax breakdown of Definition df-supp
StepHypRef Expression
1 csupp 6918 . 2
2 vx . . 3
3 vz . . 3
4 cvv 3109 . . 3
52cv 1394 . . . . . 6
6 vi . . . . . . . 8
76cv 1394 . . . . . . 7
87csn 4029 . . . . . 6
95, 8cima 5007 . . . . 5
103cv 1394 . . . . . 6
1110csn 4029 . . . . 5
129, 11wne 2652 . . . 4
135cdm 5004 . . . 4
1412, 6, 13crab 2811 . . 3
152, 3, 4, 4, 14cmpt2 6298 . 2
161, 15wceq 1395 1
Colors of variables: wff setvar class
This definition is referenced by:  suppval  6920  supp0prc  6921
  Copyright terms: Public domain W3C validator