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Metamath Proof Explorer

Theorem dmico

Description: The domain of the closed-below, open-above interval function. (Contributed by Glauco Siliprandi, 2-Jan-2022)

		Ref	Expression
	Assertion	dmico	$⊢ dom [.) = ℝ^{} \times ℝ^{}$

Step	Hyp	Ref	Expression
1		df-ico	$⊢ [.) = (x \in ℝ^{}, y \in ℝ^{} ⟼ \{z \in ℝ^{*} \| (x \leq z \land z < y)\})$
2	1	ixxf	$⊢ [.) : ℝ^{} \times ℝ^{} ⟶ 𝒫 ℝ^{*}$
3	2	fdmi	$⊢ dom [.) = ℝ^{} \times ℝ^{}$