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Metamath Proof Explorer

Theorem uzid2

Description: Membership of the least member in an upper set of integers. (Contributed by Glauco Siliprandi, 23-Oct-2021)

		Ref	Expression
	Assertion	uzid2	$⊢ M \in ℤ_{\geq N} \to M \in ℤ_{\geq M}$

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