Description: The degree of the vertex in a loop-free hypergraph with one vertex is 0. (Contributed by AV, 2-Apr-2021)
Ref | Expression | ||
---|---|---|---|
Hypotheses | vtxdlfuhgr1v.v | |
|
vtxdlfuhgr1v.i | |
||
vtxdlfuhgr1v.e | |
||
Assertion | vtxdlfuhgr1v | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vtxdlfuhgr1v.v | |
|
2 | vtxdlfuhgr1v.i | |
|
3 | vtxdlfuhgr1v.e | |
|
4 | simpl1 | |
|
5 | simpr | |
|
6 | 1 2 3 | lfuhgr1v0e | |
7 | 6 | adantr | |
8 | eqid | |
|
9 | 1 8 | vtxduhgr0e | |
10 | 4 5 7 9 | syl3anc | |
11 | 10 | ex | |