Theorem iccssred

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

	Ref	Expression
Hypotheses	iccssred.1	|- ( ph -> A e. RR )
	iccssred.2	|- ( ph -> B e. RR )
Assertion	iccssred	|- ( ph -> ( A [,] B ) C_ RR )

Proof

Step	Hyp	Ref	Expression
1		iccssred.1	|- ( ph -> A e. RR )
2		iccssred.2	|- ( ph -> B e. RR )
3		iccssre	|- ( ( A e. RR /\ B e. RR ) -> ( A [,] B ) C_ RR )
4	1 2 3	syl2anc	|- ( ph -> ( A [,] B ) C_ RR )