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 ) ) |
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 ) ) |