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	$$⊢E=\mathrm{iEdg}\left(G\right)$$
Assertion	uhgrfun	$$⊢G\in \mathrm{UHGraph}\to \mathrm{Fun}E$$

Proof

Step	Hyp	Ref	Expression
1		uhgrfun.e	$$⊢E=\mathrm{iEdg}\left(G\right)$$
2		eqid	$$⊢\mathrm{Vtx}\left(G\right)=\mathrm{Vtx}\left(G\right)$$
3	2 1	uhgrf	$$⊢G\in \mathrm{UHGraph}\to E:\mathrm{dom}E⟶𝒫\mathrm{Vtx}\left(G\right)\setminus \left\{\varnothing \right\}$$
4	3	ffund	$$⊢G\in \mathrm{UHGraph}\to \mathrm{Fun}E$$