Step |
Hyp |
Ref |
Expression |
1 |
|
3wlkd.p |
|- P = <" A B C D "> |
2 |
|
3wlkd.f |
|- F = <" J K L "> |
3 |
|
3wlkd.s |
|- ( ph -> ( ( A e. V /\ B e. V ) /\ ( C e. V /\ D e. V ) ) ) |
4 |
|
3wlkd.n |
|- ( ph -> ( ( A =/= B /\ A =/= C ) /\ ( B =/= C /\ B =/= D ) /\ C =/= D ) ) |
5 |
|
3wlkd.e |
|- ( ph -> ( { A , B } C_ ( I ` J ) /\ { B , C } C_ ( I ` K ) /\ { C , D } C_ ( I ` L ) ) ) |
6 |
1 2 3 4 5
|
3wlkdlem6 |
|- ( ph -> ( A e. ( I ` J ) /\ B e. ( I ` K ) /\ C e. ( I ` L ) ) ) |
7 |
|
elfvex |
|- ( A e. ( I ` J ) -> J e. _V ) |
8 |
|
elfvex |
|- ( B e. ( I ` K ) -> K e. _V ) |
9 |
|
elfvex |
|- ( C e. ( I ` L ) -> L e. _V ) |
10 |
7 8 9
|
3anim123i |
|- ( ( A e. ( I ` J ) /\ B e. ( I ` K ) /\ C e. ( I ` L ) ) -> ( J e. _V /\ K e. _V /\ L e. _V ) ) |
11 |
6 10
|
syl |
|- ( ph -> ( J e. _V /\ K e. _V /\ L e. _V ) ) |