Theorem elioored

Description: A member of an open interval of reals is a real. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypothesis	elioored.1	⊢ ( 𝜑 → 𝐴 ∈ ( 𝐵 (,) 𝐶 ) )
Assertion	elioored	⊢ ( 𝜑 → 𝐴 ∈ ℝ )

Proof

Step	Hyp	Ref	Expression
1		elioored.1	⊢ ( 𝜑 → 𝐴 ∈ ( 𝐵 (,) 𝐶 ) )
2		elioore	⊢ ( 𝐴 ∈ ( 𝐵 (,) 𝐶 ) → 𝐴 ∈ ℝ )
3	1 2	syl	⊢ ( 𝜑 → 𝐴 ∈ ℝ )