Theorem usgrfun

Description: The edge function of a simple graph is a function. (Contributed by Alexander van der Vekens, 18-Aug-2017) (Revised by AV, 13-Oct-2020)

	Ref	Expression
Assertion	usgrfun	|- ( G e. USGraph -> Fun ( iEdg ` G ) )

Proof

Step	Hyp	Ref	Expression
1		eqid	|- ( Vtx ` G ) = ( Vtx ` G )
2		eqid	|- ( iEdg ` G ) = ( iEdg ` G )
3	1 2	usgrfs	|- ( G e. USGraph -> ( iEdg ` G ) : dom ( iEdg ` G ) -1-1-> { x e. ~P ( Vtx ` G ) | ( # ` x ) = 2 } )
4		f1fun	|- ( ( iEdg ` G ) : dom ( iEdg ` G ) -1-1-> { x e. ~P ( Vtx ` G ) | ( # ` x ) = 2 } -> Fun ( iEdg ` G ) )
5	3 4	syl	|- ( G e. USGraph -> Fun ( iEdg ` G ) )