Metamath Proof Explorer

Theorem edguhgr

Description: An edge of a hypergraph is a subset of vertices. (Contributed by AV, 26-Oct-2020) (Proof shortened by AV, 28-Nov-2020)

Ref Expression
Assertion edguhgr ⊢G∈UHGraph∧E∈Edg⁡G→E∈𝒫Vtx⁡G

Proof

Step Hyp Ref Expression
1 uhgredgn0 ⊢G∈UHGraph∧E∈Edg⁡G→E∈𝒫Vtx⁡G∖∅
2 1 eldifad ⊢G∈UHGraph∧E∈Edg⁡G→E∈𝒫Vtx⁡G