Metamath Proof Explorer
Description: Subset relationship for two sets of upper integers. (Contributed by Glauco Siliprandi, 23-Oct-2021)
|
|
Ref |
Expression |
|
Hypothesis |
uzssd.1 |
⊢ ( 𝜑 → 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) ) |
|
Assertion |
uzssd |
⊢ ( 𝜑 → ( ℤ≥ ‘ 𝑁 ) ⊆ ( ℤ≥ ‘ 𝑀 ) ) |
Proof
Step |
Hyp |
Ref |
Expression |
1 |
|
uzssd.1 |
⊢ ( 𝜑 → 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) ) |
2 |
|
uzss |
⊢ ( 𝑁 ∈ ( ℤ≥ ‘ 𝑀 ) → ( ℤ≥ ‘ 𝑁 ) ⊆ ( ℤ≥ ‘ 𝑀 ) ) |
3 |
1 2
|
syl |
⊢ ( 𝜑 → ( ℤ≥ ‘ 𝑁 ) ⊆ ( ℤ≥ ‘ 𝑀 ) ) |