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