Theorem subgruhgrfun

Description: The edge function of a subgraph of a hypergraph is a function. (Contributed by AV, 16-Nov-2020) (Proof shortened by AV, 20-Nov-2020)

	Ref	Expression
Assertion	subgruhgrfun	⊢ ( ( 𝐺 ∈ UHGraph ∧ 𝑆 SubGraph 𝐺 ) → Fun ( iEdg ‘ 𝑆 ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ ( iEdg ‘ 𝐺 ) = ( iEdg ‘ 𝐺 )
2	1	uhgrfun	⊢ ( 𝐺 ∈ UHGraph → Fun ( iEdg ‘ 𝐺 ) )
3		subgrfun	⊢ ( ( Fun ( iEdg ‘ 𝐺 ) ∧ 𝑆 SubGraph 𝐺 ) → Fun ( iEdg ‘ 𝑆 ) )
4	2 3	sylan	⊢ ( ( 𝐺 ∈ UHGraph ∧ 𝑆 SubGraph 𝐺 ) → Fun ( iEdg ‘ 𝑆 ) )