| Step |
Hyp |
Ref |
Expression |
| 1 |
|
1wlkd.p |
|- P = <" X Y "> |
| 2 |
|
1wlkd.f |
|- F = <" J "> |
| 3 |
|
fun0 |
|- Fun (/) |
| 4 |
2
|
fveq2i |
|- ( # ` F ) = ( # ` <" J "> ) |
| 5 |
|
s1len |
|- ( # ` <" J "> ) = 1 |
| 6 |
4 5
|
eqtri |
|- ( # ` F ) = 1 |
| 7 |
6
|
oveq2i |
|- ( 1 ..^ ( # ` F ) ) = ( 1 ..^ 1 ) |
| 8 |
|
fzo0 |
|- ( 1 ..^ 1 ) = (/) |
| 9 |
7 8
|
eqtri |
|- ( 1 ..^ ( # ` F ) ) = (/) |
| 10 |
9
|
reseq2i |
|- ( P |` ( 1 ..^ ( # ` F ) ) ) = ( P |` (/) ) |
| 11 |
|
res0 |
|- ( P |` (/) ) = (/) |
| 12 |
10 11
|
eqtri |
|- ( P |` ( 1 ..^ ( # ` F ) ) ) = (/) |
| 13 |
12
|
cnveqi |
|- `' ( P |` ( 1 ..^ ( # ` F ) ) ) = `' (/) |
| 14 |
|
cnv0 |
|- `' (/) = (/) |
| 15 |
13 14
|
eqtri |
|- `' ( P |` ( 1 ..^ ( # ` F ) ) ) = (/) |
| 16 |
15
|
funeqi |
|- ( Fun `' ( P |` ( 1 ..^ ( # ` F ) ) ) <-> Fun (/) ) |
| 17 |
3 16
|
mpbir |
|- Fun `' ( P |` ( 1 ..^ ( # ` F ) ) ) |