Step |
Hyp |
Ref |
Expression |
1 |
|
1nn0 |
⊢ 1 ∈ ℕ0 |
2 |
|
fmtno |
⊢ ( 1 ∈ ℕ0 → ( FermatNo ‘ 1 ) = ( ( 2 ↑ ( 2 ↑ 1 ) ) + 1 ) ) |
3 |
1 2
|
ax-mp |
⊢ ( FermatNo ‘ 1 ) = ( ( 2 ↑ ( 2 ↑ 1 ) ) + 1 ) |
4 |
|
2cn |
⊢ 2 ∈ ℂ |
5 |
|
exp1 |
⊢ ( 2 ∈ ℂ → ( 2 ↑ 1 ) = 2 ) |
6 |
4 5
|
ax-mp |
⊢ ( 2 ↑ 1 ) = 2 |
7 |
6
|
oveq2i |
⊢ ( 2 ↑ ( 2 ↑ 1 ) ) = ( 2 ↑ 2 ) |
8 |
7
|
oveq1i |
⊢ ( ( 2 ↑ ( 2 ↑ 1 ) ) + 1 ) = ( ( 2 ↑ 2 ) + 1 ) |
9 |
|
sq2 |
⊢ ( 2 ↑ 2 ) = 4 |
10 |
9
|
oveq1i |
⊢ ( ( 2 ↑ 2 ) + 1 ) = ( 4 + 1 ) |
11 |
|
4p1e5 |
⊢ ( 4 + 1 ) = 5 |
12 |
8 10 11
|
3eqtri |
⊢ ( ( 2 ↑ ( 2 ↑ 1 ) ) + 1 ) = 5 |
13 |
3 12
|
eqtri |
⊢ ( FermatNo ‘ 1 ) = 5 |