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Metamath Proof Explorer

Theorem elfzomin

Description: Membership of an integer in the smallest open range of integers. (Contributed by Alexander van der Vekens, 22-Sep-2018)

		Ref	Expression
	Assertion	elfzomin	$⊢ Z \in ℤ \to Z \in (Z ..^Z + 1)$

Step	Hyp	Ref	Expression
1		snidg	$⊢ Z \in ℤ \to Z \in \{Z\}$
2		fzosn	$⊢ Z \in ℤ \to (Z ..^Z + 1) = \{Z\}$
3	1 2	eleqtrrd	$⊢ Z \in ℤ \to Z \in (Z ..^Z + 1)$