Theorem uzred

Description: An upper integer is a real number. (Contributed by Glauco Siliprandi, 2-Jan-2022)

	Ref	Expression
Hypotheses	uzred.1	$$⊢Z={\mathbb{Z}}_{\ge M}$$
	uzred.2	$$⊢\phi \to A\in Z$$
Assertion	uzred	$$⊢\phi \to A\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		uzred.1	$$⊢Z={\mathbb{Z}}_{\ge M}$$
2		uzred.2	$$⊢\phi \to A\in Z$$
3		zssre	$$⊢\mathbb{Z}\subseteq ℝ$$
4	1 2	eluzelz2d	$$⊢\phi \to A\in \mathbb{Z}$$
5	3 4	sseldi	$$⊢\phi \to A\in ℝ$$