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Metamath Proof Explorer

Theorem uhgrf

Description: The edge function of an undirected hypergraph is a function into the power set of the set of vertices. (Contributed by Alexander van der Vekens, 26-Dec-2017) (Revised by AV, 9-Oct-2020)

	Ref	Expression
Hypotheses	uhgrf.v	⊢ 𝑉 = ( Vtx ‘ 𝐺 )
	uhgrf.e	⊢ 𝐸 = ( iEdg ‘ 𝐺 )
Assertion	uhgrf	⊢ ( 𝐺 ∈ UHGraph → 𝐸 : dom 𝐸 ⟶ ( 𝒫 𝑉 ∖ { ∅ } ) )

Proof

Step	Hyp	Ref	Expression
1		uhgrf.v	⊢ 𝑉 = ( Vtx ‘ 𝐺 )
2		uhgrf.e	⊢ 𝐸 = ( iEdg ‘ 𝐺 )
3	1 2	isuhgr	⊢ ( 𝐺 ∈ UHGraph → ( 𝐺 ∈ UHGraph ↔ 𝐸 : dom 𝐸 ⟶ ( 𝒫 𝑉 ∖ { ∅ } ) ) )
4	3	ibi	⊢ ( 𝐺 ∈ UHGraph → 𝐸 : dom 𝐸 ⟶ ( 𝒫 𝑉 ∖ { ∅ } ) )