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	$$⊢\left[A,B\right)\subseteq {ℝ}^{*}$$

Proof

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