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Metamath Proof Explorer

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