Description: The set of vertices of a graph represented as an ordered pair of vertices and indexed edges. (Contributed by AV, 9-Jan-2020) (Revised by AV, 21-Sep-2020)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | opvtxval | |- ( G e. ( _V X. _V ) -> ( Vtx ` G ) = ( 1st ` G ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | vtxval | |- ( Vtx ` G ) = if ( G e. ( _V X. _V ) , ( 1st ` G ) , ( Base ` G ) ) |
|
| 2 | iftrue | |- ( G e. ( _V X. _V ) -> if ( G e. ( _V X. _V ) , ( 1st ` G ) , ( Base ` G ) ) = ( 1st ` G ) ) |
|
| 3 | 1 2 | syl5eq | |- ( G e. ( _V X. _V ) -> ( Vtx ` G ) = ( 1st ` G ) ) |