Theorem uhgredgss

Description: The set of edges of a hypergraph is a subset of the power set of vertices without the empty set. (Contributed by AV, 29-Nov-2020)

	Ref	Expression
Assertion	uhgredgss	⊢ ( 𝐺 ∈ UHGraph → ( Edg ‘ 𝐺 ) ⊆ ( 𝒫 ( Vtx ‘ 𝐺 ) ∖ { ∅ } ) )

Proof

Step	Hyp	Ref	Expression
1		uhgredgn0	⊢ ( ( 𝐺 ∈ UHGraph ∧ 𝑥 ∈ ( Edg ‘ 𝐺 ) ) → 𝑥 ∈ ( 𝒫 ( Vtx ‘ 𝐺 ) ∖ { ∅ } ) )
2	1	ex	⊢ ( 𝐺 ∈ UHGraph → ( 𝑥 ∈ ( Edg ‘ 𝐺 ) → 𝑥 ∈ ( 𝒫 ( Vtx ‘ 𝐺 ) ∖ { ∅ } ) ) )
3	2	ssrdv	⊢ ( 𝐺 ∈ UHGraph → ( Edg ‘ 𝐺 ) ⊆ ( 𝒫 ( Vtx ‘ 𝐺 ) ∖ { ∅ } ) )