Description: A simple graph with two vertices is an acyclic graph. (Contributed by BTernaryTau, 12-Oct-2023)
Ref | Expression | ||
---|---|---|---|
Hypothesis | acycgrv.1 | |
|
Assertion | acycgr2v | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | acycgrv.1 | |
|
2 | 1 | usgrcyclgt2v | |
3 | 2re | |
|
4 | 3 | rexri | |
5 | 1 | fvexi | |
6 | hashxrcl | |
|
7 | 5 6 | ax-mp | |
8 | xrltne | |
|
9 | 4 7 8 | mp3an12 | |
10 | 9 | neneqd | |
11 | 2 10 | syl | |
12 | 11 | 3expib | |
13 | 12 | con2d | |
14 | 13 | imp | |
15 | 14 | nexdv | |
16 | 15 | nexdv | |
17 | isacycgr | |
|
18 | 17 | adantr | |
19 | 16 18 | mpbird | |