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	⊢ ( 𝐴 (,] 𝐵 ) ⊆ ℝ*

Proof

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