Theorem uhgredgiedgb

Description: In a hypergraph, a set is an edge iff it is an indexed edge. (Contributed by AV, 17-Oct-2020)

	Ref	Expression
Hypothesis	uhgredgiedgb.i	|- I = ( iEdg ` G )
Assertion	uhgredgiedgb	|- ( G e. UHGraph -> ( E e. ( Edg ` G ) <-> E. x e. dom I E = ( I ` x ) ) )

Proof

Step	Hyp	Ref	Expression
1		uhgredgiedgb.i	|- I = ( iEdg ` G )
2	1	uhgrfun	|- ( G e. UHGraph -> Fun I )
3	1	edgiedgb	|- ( Fun I -> ( E e. ( Edg ` G ) <-> E. x e. dom I E = ( I ` x ) ) )
4	2 3	syl	|- ( G e. UHGraph -> ( E e. ( Edg ` G ) <-> E. x e. dom I E = ( I ` x ) ) )