Step |
Hyp |
Ref |
Expression |
1 |
|
wrdf |
|- ( S e. Word A -> S : ( 0 ..^ ( # ` S ) ) --> A ) |
2 |
|
fimadmfo |
|- ( S : ( 0 ..^ ( # ` S ) ) --> A -> S : ( 0 ..^ ( # ` S ) ) -onto-> ( S " ( 0 ..^ ( # ` S ) ) ) ) |
3 |
|
fof |
|- ( S : ( 0 ..^ ( # ` S ) ) -onto-> ( S " ( 0 ..^ ( # ` S ) ) ) -> S : ( 0 ..^ ( # ` S ) ) --> ( S " ( 0 ..^ ( # ` S ) ) ) ) |
4 |
1 2 3
|
3syl |
|- ( S e. Word A -> S : ( 0 ..^ ( # ` S ) ) --> ( S " ( 0 ..^ ( # ` S ) ) ) ) |
5 |
|
iswrdb |
|- ( S e. Word ( S " ( 0 ..^ ( # ` S ) ) ) <-> S : ( 0 ..^ ( # ` S ) ) --> ( S " ( 0 ..^ ( # ` S ) ) ) ) |
6 |
4 5
|
sylibr |
|- ( S e. Word A -> S e. Word ( S " ( 0 ..^ ( # ` S ) ) ) ) |