Theorem iccssred

Description: A closed real interval is a set of reals. (Contributed by Glauco Siliprandi, 11-Dec-2019)

	Ref	Expression
Hypotheses	iccssred.1	$$⊢\phi \to A\in ℝ$$
	iccssred.2	$$⊢\phi \to B\in ℝ$$
Assertion	iccssred	$$⊢\phi \to \left[A,B\right]\subseteq ℝ$$

Proof

Step	Hyp	Ref	Expression
1		iccssred.1	$$⊢\phi \to A\in ℝ$$
2		iccssred.2	$$⊢\phi \to B\in ℝ$$
3		iccssre	$$⊢\left(A\in ℝ\wedge B\in ℝ\right)\to \left[A,B\right]\subseteq ℝ$$
4	1 2 3	syl2anc	$$⊢\phi \to \left[A,B\right]\subseteq ℝ$$