| Step |
Hyp |
Ref |
Expression |
| 1 |
|
uhgrspan1.v |
|- V = ( Vtx ` G ) |
| 2 |
|
uhgrspan1.i |
|- I = ( iEdg ` G ) |
| 3 |
|
uhgrspan1.f |
|- F = { i e. dom I | N e/ ( I ` i ) } |
| 4 |
|
uhgrspan1.s |
|- S = <. ( V \ { N } ) , ( I |` F ) >. |
| 5 |
4
|
fveq2i |
|- ( iEdg ` S ) = ( iEdg ` <. ( V \ { N } ) , ( I |` F ) >. ) |
| 6 |
1 2 3
|
uhgrspan1lem1 |
|- ( ( V \ { N } ) e. _V /\ ( I |` F ) e. _V ) |
| 7 |
|
opiedgfv |
|- ( ( ( V \ { N } ) e. _V /\ ( I |` F ) e. _V ) -> ( iEdg ` <. ( V \ { N } ) , ( I |` F ) >. ) = ( I |` F ) ) |
| 8 |
6 7
|
ax-mp |
|- ( iEdg ` <. ( V \ { N } ) , ( I |` F ) >. ) = ( I |` F ) |
| 9 |
5 8
|
eqtri |
|- ( iEdg ` S ) = ( I |` F ) |