Theorem uhgrfun

Description: The edge function of an undirected hypergraph is a function. (Contributed by Alexander van der Vekens, 26-Dec-2017) (Revised by AV, 15-Dec-2020)

	Ref	Expression
Hypothesis	uhgrfun.e	⊢ 𝐸 = ( iEdg ‘ 𝐺 )
Assertion	uhgrfun	⊢ ( 𝐺 ∈ UHGraph → Fun 𝐸 )

Proof

Step	Hyp	Ref	Expression
1		uhgrfun.e	⊢ 𝐸 = ( iEdg ‘ 𝐺 )
2		eqid	⊢ ( Vtx ‘ 𝐺 ) = ( Vtx ‘ 𝐺 )
3	2 1	uhgrf	⊢ ( 𝐺 ∈ UHGraph → 𝐸 : dom 𝐸 ⟶ ( 𝒫 ( Vtx ‘ 𝐺 ) ∖ { ∅ } ) )
4	3	ffund	⊢ ( 𝐺 ∈ UHGraph → Fun 𝐸 )