Theorem ioossre

Description: An open interval is a set of reals. (Contributed by NM, 31-May-2007)

	Ref	Expression
Assertion	ioossre	⊢ ( 𝐴 (,) 𝐵 ) ⊆ ℝ

Proof

Step	Hyp	Ref	Expression
1		elioore	⊢ ( 𝑥 ∈ ( 𝐴 (,) 𝐵 ) → 𝑥 ∈ ℝ )
2	1	ssriv	⊢ ( 𝐴 (,) 𝐵 ) ⊆ ℝ