Theorem iccssxr

Description: A closed interval is a set of extended reals. (Contributed by FL, 28-Jul-2008) (Revised by Mario Carneiro, 4-Jul-2014)

	Ref	Expression
Assertion	iccssxr	$$⊢\left[A,B\right]\subseteq {ℝ}^{*}$$

Proof

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