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Metamath Proof Explorer

Theorem eluzfz

Description: Membership in a finite set of sequential integers. (Contributed by NM, 4-Oct-2005) (Revised by Mario Carneiro, 28-Apr-2015)

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

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	biimpri	$⊢ (K \in ℤ_{\geq M} \land N \in ℤ_{\geq K}) \to K \in (M \dots N)$