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 ∈ ( 𝐵 [,] 𝐶 ) → 𝐴 ∈ ℝ* )

Proof

Step	Hyp	Ref	Expression
1		iccssxr	⊢ ( 𝐵 [,] 𝐶 ) ⊆ ℝ*
2	1	sseli	⊢ ( 𝐴 ∈ ( 𝐵 [,] 𝐶 ) → 𝐴 ∈ ℝ* )