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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	$⊢ Z = ℤ_{\geq M}$
	Assertion	uzssre2	$⊢ Z \subseteq ℝ$

Step	Hyp	Ref	Expression
1		uzssre2.1	$⊢ Z = ℤ_{\geq M}$
2		uzssz	$⊢ ℤ_{\geq M} \subseteq ℤ$
3		zssre	$⊢ ℤ \subseteq ℝ$
4	2 3	sstri	$⊢ ℤ_{\geq M} \subseteq ℝ$
5	1 4	eqsstri	$⊢ Z \subseteq ℝ$