Theorem eluzelre

Description: A member of an upper set of integers is a real. (Contributed by Mario Carneiro, 31-Aug-2013)

	Ref	Expression
Assertion	eluzelre	$$⊢N\in {\mathbb{Z}}_{\ge M}\to N\in ℝ$$

Proof

Step	Hyp	Ref	Expression
1		eluzelz	$$⊢N\in {\mathbb{Z}}_{\ge M}\to N\in \mathbb{Z}$$
2	1	zred	$$⊢N\in {\mathbb{Z}}_{\ge M}\to N\in ℝ$$