Theorem eliccxr

Description: A member of a closed interval is an extended real. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Assertion	eliccxr	$$⊢A\in \left[B,C\right]\to A\in {ℝ}^{*}$$

Proof

Step	Hyp	Ref	Expression
1		iccssxr	$$⊢\left[B,C\right]\subseteq {ℝ}^{*}$$
2	1	sseli	$$⊢A\in \left[B,C\right]\to A\in {ℝ}^{*}$$