Description: Any null graph (without vertices and edges) is a friendship graph. (Contributed by Alexander van der Vekens, 30-Sep-2017) (Revised by AV, 29-Mar-2021)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | frgr0vb | |- ( ( G e. W /\ ( Vtx ` G ) = (/) /\ ( iEdg ` G ) = (/) ) -> G e. FriendGraph ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | frgr0v | |- ( ( G e. W /\ ( Vtx ` G ) = (/) ) -> ( G e. FriendGraph <-> ( iEdg ` G ) = (/) ) ) |
|
| 2 | 1 | biimp3ar | |- ( ( G e. W /\ ( Vtx ` G ) = (/) /\ ( iEdg ` G ) = (/) ) -> G e. FriendGraph ) |