Description: The class of simple graphs is a proper class (and therefore, because of prcssprc , the classes of multigraphs, pseudographs and hypergraphs are proper classes, too). (Contributed by AV, 27-Dec-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | usgrprc | |- USGraph e/ _V |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid | |- { <. v , e >. | e : (/) --> (/) } = { <. v , e >. | e : (/) --> (/) } |
|
2 | 1 | griedg0ssusgr | |- { <. v , e >. | e : (/) --> (/) } C_ USGraph |
3 | 1 | griedg0prc | |- { <. v , e >. | e : (/) --> (/) } e/ _V |
4 | prcssprc | |- ( ( { <. v , e >. | e : (/) --> (/) } C_ USGraph /\ { <. v , e >. | e : (/) --> (/) } e/ _V ) -> USGraph e/ _V ) |
|
5 | 2 3 4 | mp2an | |- USGraph e/ _V |