Metamath Proof Explorer
Description: A member of an upper set of integers is an integer. (Contributed by Glauco Siliprandi, 23-Oct-2021)
|
|
Ref |
Expression |
|
Hypotheses |
eluzelz2d.1 |
⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 ) |
|
|
eluzelz2d.2 |
⊢ ( 𝜑 → 𝑁 ∈ 𝑍 ) |
|
Assertion |
eluzelz2d |
⊢ ( 𝜑 → 𝑁 ∈ ℤ ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
eluzelz2d.1 |
⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 ) |
2 |
|
eluzelz2d.2 |
⊢ ( 𝜑 → 𝑁 ∈ 𝑍 ) |
3 |
1
|
eluzelz2 |
⊢ ( 𝑁 ∈ 𝑍 → 𝑁 ∈ ℤ ) |
4 |
2 3
|
syl |
⊢ ( 𝜑 → 𝑁 ∈ ℤ ) |