| Step |
Hyp |
Ref |
Expression |
| 1 |
|
2wlkd.p |
|- P = <" A B C "> |
| 2 |
|
2wlkd.f |
|- F = <" J K "> |
| 3 |
|
2wlkd.s |
|- ( ph -> ( A e. V /\ B e. V /\ C e. V ) ) |
| 4 |
|
2wlkd.n |
|- ( ph -> ( A =/= B /\ B =/= C ) ) |
| 5 |
|
2wlkd.e |
|- ( ph -> ( { A , B } C_ ( I ` J ) /\ { B , C } C_ ( I ` K ) ) ) |
| 6 |
1 2 3 4 5
|
2wlkdlem6 |
|- ( ph -> ( B e. ( I ` J ) /\ B e. ( I ` K ) ) ) |
| 7 |
|
elfvex |
|- ( B e. ( I ` J ) -> J e. _V ) |
| 8 |
|
elfvex |
|- ( B e. ( I ` K ) -> K e. _V ) |
| 9 |
7 8
|
anim12i |
|- ( ( B e. ( I ` J ) /\ B e. ( I ` K ) ) -> ( J e. _V /\ K e. _V ) ) |
| 10 |
6 9
|
syl |
|- ( ph -> ( J e. _V /\ K e. _V ) ) |