This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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	$⊢ N \in ℤ_{\geq M} \to N \in ℝ$

Step	Hyp	Ref	Expression
1		eluzelz	$⊢ N \in ℤ_{\geq M} \to N \in ℤ$
2	1	zred	$⊢ N \in ℤ_{\geq M} \to N \in ℝ$