Metamath Proof Explorer
Description: A 1-based half-open integer interval up to, but not including, 2 is a
singleton. (Contributed by Alexander van der Vekens, 31-Jan-2018)
|
|
Ref |
Expression |
|
Assertion |
fzo12sn |
⊢ ( 1 ..^ 2 ) = { 1 } |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
df-2 |
⊢ 2 = ( 1 + 1 ) |
2 |
1
|
oveq2i |
⊢ ( 1 ..^ 2 ) = ( 1 ..^ ( 1 + 1 ) ) |
3 |
|
1z |
⊢ 1 ∈ ℤ |
4 |
|
fzosn |
⊢ ( 1 ∈ ℤ → ( 1 ..^ ( 1 + 1 ) ) = { 1 } ) |
5 |
3 4
|
ax-mp |
⊢ ( 1 ..^ ( 1 + 1 ) ) = { 1 } |
6 |
2 5
|
eqtri |
⊢ ( 1 ..^ 2 ) = { 1 } |