Description: The null graph, with no vertices, is a simple graph iff the edge function is empty. (Contributed by Alexander van der Vekens, 30-Sep-2017) (Revised by AV, 16-Oct-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | usgr0vb | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | usgruhgr | |
|
2 | uhgr0vb | |
|
3 | 1 2 | syl5ib | |
4 | simpl | |
|
5 | simpr | |
|
6 | 4 5 | usgr0e | |
7 | 6 | ex | |
8 | 7 | adantr | |
9 | 3 8 | impbid | |