Description: A class X is not a neighbor of itself (whether it is a vertex or not). (Contributed by Alexander van der Vekens, 12-Oct-2017) (Revised by AV, 3-Nov-2020) (Revised by AV, 12-Feb-2022)
Ref | Expression | ||
---|---|---|---|
Assertion | nbgrnself2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | id | |
|
2 | oveq2 | |
|
3 | 1 2 | neleq12d | |
4 | eqid | |
|
5 | 4 | nbgrnself | |
6 | 3 5 | vtoclri | |
7 | 4 | nbgrisvtx | |
8 | 7 | con3i | |
9 | df-nel | |
|
10 | 8 9 | sylibr | |
11 | 6 10 | pm2.61i | |