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	$$⊢V=\mathrm{Vtx}\left(G\right)$$
	uhgrf.e	$$⊢E=\mathrm{iEdg}\left(G\right)$$
Assertion	uhgrf	$$⊢G\in \mathrm{UHGraph}\to E:\mathrm{dom}E⟶𝒫V\setminus \left\{\varnothing \right\}$$

Proof

Step	Hyp	Ref	Expression
1		uhgrf.v	$$⊢V=\mathrm{Vtx}\left(G\right)$$
2		uhgrf.e	$$⊢E=\mathrm{iEdg}\left(G\right)$$
3	1 2	isuhgr	$$⊢G\in \mathrm{UHGraph}\to \left(G\in \mathrm{UHGraph}\leftrightarrow E:\mathrm{dom}E⟶𝒫V\setminus \left\{\varnothing \right\}\right)$$
4	3	ibi	$$⊢G\in \mathrm{UHGraph}\to E:\mathrm{dom}E⟶𝒫V\setminus \left\{\varnothing \right\}$$