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Metamath Proof Explorer

Theorem icossxr

Description: A closed-below, open-above interval is a subset of the extended reals. (Contributed by FL, 29-May-2014) (Revised by Mario Carneiro, 4-Jul-2014)

		Ref	Expression
	Assertion	icossxr	$⊢ [A, B) \subseteq ℝ^{*}$

Proof

Step	Hyp	Ref	Expression
1		df-ico	$⊢ [.) = (x \in ℝ^{}, y \in ℝ^{} ⟼ \{z \in ℝ^{*} \| (x \leq z \land z < y)\})$
2	1	ixxssxr	$⊢ [A, B) \subseteq ℝ^{*}$