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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	$⊢ G \in UHGraph \to E : dom E ⟶ 𝒫 V ∖ \{\emptyset\}$

Proof

Step	Hyp	Ref	Expression
1		uhgrf.v	$⊢ V = Vtx (G)$
2		uhgrf.e	$⊢ E = iEdg (G)$
3	1 2	isuhgr	$⊢ G \in UHGraph \to (G \in UHGraph \leftrightarrow E : dom E ⟶ 𝒫 V ∖ \{\emptyset\})$
4	3	ibi	$⊢ G \in UHGraph \to E : dom E ⟶ 𝒫 V ∖ \{\emptyset\}$