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Definition df-uhgr 25866
Description: Define the class of all undirected hypergraphs. An undirected hypergraph consists of a set 𝑣 (of "vertices") and a function 𝑒 (representing indexed "edges") into the powerset of this set (the empty set excluded). (Contributed by Alexander van der Vekens, 26-Dec-2017.) (Revised by AV, 8-Oct-2020.)
Assertion
Ref Expression
df-uhgr UHGraph = {𝑔[(Vtx‘𝑔) / 𝑣][(iEdg‘𝑔) / 𝑒]𝑒:dom 𝑒⟶(𝒫 𝑣 ∖ {∅})}
Distinct variable group:   𝑒,𝑔,𝑣

Detailed syntax breakdown of Definition df-uhgr
StepHypRef Expression
1 cuhgr 25864 . 2 class UHGraph
2 ve . . . . . . . 8 setvar 𝑒
32cv 1479 . . . . . . 7 class 𝑒
43cdm 5079 . . . . . 6 class dom 𝑒
5 vv . . . . . . . . 9 setvar 𝑣
65cv 1479 . . . . . . . 8 class 𝑣
76cpw 4135 . . . . . . 7 class 𝒫 𝑣
8 c0 3896 . . . . . . . 8 class
98csn 4153 . . . . . . 7 class {∅}
107, 9cdif 3556 . . . . . 6 class (𝒫 𝑣 ∖ {∅})
114, 10, 3wf 5848 . . . . 5 wff 𝑒:dom 𝑒⟶(𝒫 𝑣 ∖ {∅})
12 vg . . . . . . 7 setvar 𝑔
1312cv 1479 . . . . . 6 class 𝑔
14 ciedg 25792 . . . . . 6 class iEdg
1513, 14cfv 5852 . . . . 5 class (iEdg‘𝑔)
1611, 2, 15wsbc 3421 . . . 4 wff [(iEdg‘𝑔) / 𝑒]𝑒:dom 𝑒⟶(𝒫 𝑣 ∖ {∅})
17 cvtx 25791 . . . . 5 class Vtx
1813, 17cfv 5852 . . . 4 class (Vtx‘𝑔)
1916, 5, 18wsbc 3421 . . 3 wff [(Vtx‘𝑔) / 𝑣][(iEdg‘𝑔) / 𝑒]𝑒:dom 𝑒⟶(𝒫 𝑣 ∖ {∅})
2019, 12cab 2607 . 2 class {𝑔[(Vtx‘𝑔) / 𝑣][(iEdg‘𝑔) / 𝑒]𝑒:dom 𝑒⟶(𝒫 𝑣 ∖ {∅})}
211, 20wceq 1480 1 wff UHGraph = {𝑔[(Vtx‘𝑔) / 𝑣][(iEdg‘𝑔) / 𝑒]𝑒:dom 𝑒⟶(𝒫 𝑣 ∖ {∅})}
Colors of variables: wff setvar class
This definition is referenced by:  isuhgr  25868
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