Metamath Proof Explorer


Theorem fzssuz

Description: A finite set of sequential integers is a subset of an upper set of integers. (Contributed by NM, 28-Oct-2005)

Ref Expression
Assertion fzssuz ( 𝑀 ... 𝑁 ) ⊆ ( ℤ≥ ‘ 𝑀 )

Proof

Step Hyp Ref Expression
1 elfzuz ⊢ ( 𝑘 ∈ ( 𝑀 ... 𝑁 ) → 𝑘 ∈ ( ℤ≥ ‘ 𝑀 ) )
2 1 ssriv ⊢ ( 𝑀 ... 𝑁 ) ⊆ ( ℤ≥ ‘ 𝑀 )