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Definition df-uhgra 25587
Description: Define the class of all undirected hypergraphs. An undirected hypergraph is a pair of a set and a function into the powerset of this set (the empty set excluded). (Contributed by Alexander van der Vekens, 26-Dec-2017.)
Assertion
Ref Expression
df-uhgra UHGrph = {⟨𝑣, 𝑒⟩ ∣ 𝑒:dom 𝑒⟶(𝒫 𝑣 ∖ {∅})}
Distinct variable group:   𝑣,𝑒

Detailed syntax breakdown of Definition df-uhgra
StepHypRef Expression
1 cuhg 25585 . 2 class UHGrph
2 ve . . . . . 6 setvar 𝑒
32cv 1473 . . . . 5 class 𝑒
43cdm 5028 . . . 4 class dom 𝑒
5 vv . . . . . . 7 setvar 𝑣
65cv 1473 . . . . . 6 class 𝑣
76cpw 4107 . . . . 5 class 𝒫 𝑣
8 c0 3873 . . . . . 6 class
98csn 4124 . . . . 5 class {∅}
107, 9cdif 3536 . . . 4 class (𝒫 𝑣 ∖ {∅})
114, 10, 3wf 5786 . . 3 wff 𝑒:dom 𝑒⟶(𝒫 𝑣 ∖ {∅})
1211, 5, 2copab 4636 . 2 class {⟨𝑣, 𝑒⟩ ∣ 𝑒:dom 𝑒⟶(𝒫 𝑣 ∖ {∅})}
131, 12wceq 1474 1 wff UHGrph = {⟨𝑣, 𝑒⟩ ∣ 𝑒:dom 𝑒⟶(𝒫 𝑣 ∖ {∅})}
Colors of variables: wff setvar class
This definition is referenced by:  reluhgra  25589  isuhgra  25593  uhgrac  25600
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