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Metamath Proof Explorer

Theorem uzssre2

Description: An upper set of integers is a subset of the Reals. (Contributed by Glauco Siliprandi, 23-Oct-2021)

Ref Expression
Hypothesis uzssre2.1 ⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 )
Assertion uzssre2 𝑍 ⊆ ℝ

Proof

Step Hyp Ref Expression
1 uzssre2.1 ⊢ 𝑍 = ( ℤ≥ ‘ 𝑀 )
2 uzssz ⊢ ( ℤ≥ ‘ 𝑀 ) ⊆ ℤ
3 zssre ⊢ ℤ ⊆ ℝ
4 2 3 sstri ⊢ ( ℤ≥ ‘ 𝑀 ) ⊆ ℝ
5 1 4 eqsstri ⊢ 𝑍 ⊆ ℝ