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Definition df-supp 7841
 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 supp = (𝑥 ∈ V, 𝑧 ∈ V ↦ {𝑖 ∈ dom 𝑥 ∣ (𝑥 “ {𝑖}) ≠ {𝑧}})
Distinct variable group:   𝑥,𝑖,𝑧

Detailed syntax breakdown of Definition df-supp
StepHypRef Expression
1 csupp 7840 . 2 class supp
2 vx . . 3 setvar 𝑥
3 vz . . 3 setvar 𝑧
4 cvv 3409 . . 3 class V
52cv 1537 . . . . . 6 class 𝑥
6 vi . . . . . . . 8 setvar 𝑖
76cv 1537 . . . . . . 7 class 𝑖
87csn 4525 . . . . . 6 class {𝑖}
95, 8cima 5530 . . . . 5 class (𝑥 “ {𝑖})
103cv 1537 . . . . . 6 class 𝑧
1110csn 4525 . . . . 5 class {𝑧}
129, 11wne 2951 . . . 4 wff (𝑥 “ {𝑖}) ≠ {𝑧}
135cdm 5527 . . . 4 class dom 𝑥
1412, 6, 13crab 3074 . . 3 class {𝑖 ∈ dom 𝑥 ∣ (𝑥 “ {𝑖}) ≠ {𝑧}}
152, 3, 4, 4, 14cmpo 7157 . 2 class (𝑥 ∈ V, 𝑧 ∈ V ↦ {𝑖 ∈ dom 𝑥 ∣ (𝑥 “ {𝑖}) ≠ {𝑧}})
161, 15wceq 1538 1 wff supp = (𝑥 ∈ V, 𝑧 ∈ V ↦ {𝑖 ∈ dom 𝑥 ∣ (𝑥 “ {𝑖}) ≠ {𝑧}})
 Colors of variables: wff setvar class This definition is referenced by:  suppval  7842  supp0prc  7843
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