Theorem iccgelbd

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

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

Proof

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