Theorem iocssxr

Description: An open-below, closed-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	iocssxr	$$⊢\left(A,B\right]\subseteq {ℝ}^{*}$$

Proof

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