Theorem iccssred

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

	Ref	Expression
Hypotheses	iccssred.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
	iccssred.2	⊢ ( 𝜑 → 𝐵 ∈ ℝ )
Assertion	iccssred	⊢ ( 𝜑 → ( 𝐴 [,] 𝐵 ) ⊆ ℝ )

Proof

Step	Hyp	Ref	Expression
1		iccssred.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		iccssred.2	⊢ ( 𝜑 → 𝐵 ∈ ℝ )
3		iccssre	⊢ ( ( 𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ ) → ( 𝐴 [,] 𝐵 ) ⊆ ℝ )
4	1 2 3	syl2anc	⊢ ( 𝜑 → ( 𝐴 [,] 𝐵 ) ⊆ ℝ )