Description: Degenerated case 1 for vertices: The set of vertices of the empty set is the empty set. (Contributed by AV, 24-Sep-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | vtxval0 | |- ( Vtx ` (/) ) = (/) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 0nelxp | |- -. (/) e. ( _V X. _V ) |
|
2 | 1 | iffalsei | |- if ( (/) e. ( _V X. _V ) , ( 1st ` (/) ) , ( Base ` (/) ) ) = ( Base ` (/) ) |
3 | vtxval | |- ( Vtx ` (/) ) = if ( (/) e. ( _V X. _V ) , ( 1st ` (/) ) , ( Base ` (/) ) ) |
|
4 | base0 | |- (/) = ( Base ` (/) ) |
|
5 | 2 3 4 | 3eqtr4i | |- ( Vtx ` (/) ) = (/) |