Step |
Hyp |
Ref |
Expression |
1 |
|
fz1ssfz0 |
|- ( 1 ... N ) C_ ( 0 ... N ) |
2 |
|
ssrin |
|- ( ( 1 ... N ) C_ ( 0 ... N ) -> ( ( 1 ... N ) i^i ( ZZ>= ` ( N + 1 ) ) ) C_ ( ( 0 ... N ) i^i ( ZZ>= ` ( N + 1 ) ) ) ) |
3 |
1 2
|
ax-mp |
|- ( ( 1 ... N ) i^i ( ZZ>= ` ( N + 1 ) ) ) C_ ( ( 0 ... N ) i^i ( ZZ>= ` ( N + 1 ) ) ) |
4 |
|
nn0disj |
|- ( ( 0 ... N ) i^i ( ZZ>= ` ( N + 1 ) ) ) = (/) |
5 |
|
sseq0 |
|- ( ( ( ( 1 ... N ) i^i ( ZZ>= ` ( N + 1 ) ) ) C_ ( ( 0 ... N ) i^i ( ZZ>= ` ( N + 1 ) ) ) /\ ( ( 0 ... N ) i^i ( ZZ>= ` ( N + 1 ) ) ) = (/) ) -> ( ( 1 ... N ) i^i ( ZZ>= ` ( N + 1 ) ) ) = (/) ) |
6 |
3 4 5
|
mp2an |
|- ( ( 1 ... N ) i^i ( ZZ>= ` ( N + 1 ) ) ) = (/) |