Description: If a vertex is adjacent to two different vertices in a simple graph, there are more than one edges starting at this vertex. (Contributed by Alexander van der Vekens, 10-Dec-2017) (Revised by AV, 17-Oct-2020) (Proof shortened by AV, 11-Feb-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | usgrf1oedg.i | |
|
usgrf1oedg.e | |
||
Assertion | usgr2edg | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | usgrf1oedg.i | |
|
2 | usgrf1oedg.e | |
|
3 | usgrumgr | |
|
4 | 1 2 | umgr2edg | |
5 | 3 4 | sylanl1 | |