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	⊢ ( 𝐴 [,) 𝐵 ) ⊆ ℝ*

Proof

Step	Hyp	Ref	Expression
1		df-ico	⊢ [,) = ( 𝑥 ∈ ℝ* , 𝑦 ∈ ℝ* ↦ { 𝑧 ∈ ℝ* ∣ ( 𝑥 ≤ 𝑧 ∧ 𝑧 < 𝑦 ) } )
2	1	ixxssxr	⊢ ( 𝐴 [,) 𝐵 ) ⊆ ℝ*