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Metamath Proof Explorer

Theorem elfzuz

Description: A member of a finite set of sequential integers belongs to an upper set of integers. (Contributed by NM, 17-Sep-2005) (Revised by Mario Carneiro, 28-Apr-2015)

		Ref	Expression
	Assertion	elfzuz	$⊢ K \in (M \dots N) \to K \in ℤ_{\geq M}$

Proof

Step	Hyp	Ref	Expression
1		elfzuzb	$⊢ K \in (M \dots N) \leftrightarrow (K \in ℤ_{\geq M} \land N \in ℤ_{\geq K})$
2	1	simplbi	$⊢ K \in (M \dots N) \to K \in ℤ_{\geq M}$