This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.
Metamath Proof Explorer
Description: A finite set of sequential integers that is a subset of NN0 .
(Contributed by Glauco Siliprandi, 5-Apr-2020)
|
|
Ref |
Expression |
|
Assertion |
fzssnn0 |
⊢ ( 0 ... 𝑁 ) ⊆ ℕ0 |
Proof
| Step |
Hyp |
Ref |
Expression |
| 1 |
|
fzssuz |
⊢ ( 0 ... 𝑁 ) ⊆ ( ℤ≥ ‘ 0 ) |
| 2 |
|
nn0uz |
⊢ ℕ0 = ( ℤ≥ ‘ 0 ) |
| 3 |
2
|
eqcomi |
⊢ ( ℤ≥ ‘ 0 ) = ℕ0 |
| 4 |
1 3
|
sseqtri |
⊢ ( 0 ... 𝑁 ) ⊆ ℕ0 |