Description: For a vertex incident to an edge there is exactly one other vertex incident to the edge in a simple pseudograph. (Contributed by AV, 18-Oct-2020) (Revised by AV, 6-Dec-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | uspgredg2vtxeu | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | uspgrupgr | |
|
2 | eqid | |
|
3 | eqid | |
|
4 | 2 3 | upgredg2vtx | |
5 | 1 4 | syl3an1 | |
6 | eqtr2 | |
|
7 | vex | |
|
8 | vex | |
|
9 | 7 8 | preqr2 | |
10 | 6 9 | syl | |
11 | 10 | a1i | |
12 | 11 | ralrimivva | |
13 | preq2 | |
|
14 | 13 | eqeq2d | |
15 | 14 | reu4 | |
16 | 5 12 15 | sylanbrc | |