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Metamath Proof Explorer

Theorem eluzelzd

Description: A member of an upper set of integers is an integer. (Contributed by Glauco Siliprandi, 8-Apr-2021)

		Ref	Expression
	Hypothesis	eluzelzd.1	$⊢ φ \to N \in ℤ_{\geq M}$
	Assertion	eluzelzd	$⊢ φ \to N \in ℤ$

Step	Hyp	Ref	Expression
1		eluzelzd.1	$⊢ φ \to N \in ℤ_{\geq M}$
2		eluzelz	$⊢ N \in ℤ_{\geq M} \to N \in ℤ$
3	1 2	syl	$⊢ φ \to N \in ℤ$