Theorem iccleubd

Description: An element of a closed interval is less than or equal to its upper bound. (Contributed by Glauco Siliprandi, 26-Jun-2021)

	Ref	Expression
Hypotheses	iccleubd.1	|- ( ph -> A e. RR* )
	iccleubd.2	|- ( ph -> B e. RR* )
	iccleubd.3	|- ( ph -> C e. ( A [,] B ) )
Assertion	iccleubd	|- ( ph -> C <_ B )

Proof

Step	Hyp	Ref	Expression
1		iccleubd.1	|- ( ph -> A e. RR* )
2		iccleubd.2	|- ( ph -> B e. RR* )
3		iccleubd.3	|- ( ph -> C e. ( A [,] B ) )
4		iccleub	|- ( ( A e. RR* /\ B e. RR* /\ C e. ( A [,] B ) ) -> C <_ B )
5	1 2 3 4	syl3anc	|- ( ph -> C <_ B )