This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

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	$⊢ φ \to A \in (B, C)$
	Assertion	elioored	$⊢ φ \to A \in ℝ$

Step	Hyp	Ref	Expression
1		elioored.1	$⊢ φ \to A \in (B, C)$
2		elioore	$⊢ A \in (B, C) \to A \in ℝ$
3	1 2	syl	$⊢ φ \to A \in ℝ$