Proving that a statement about $<$ is valid I need to do assignment for my homework, in which I need to prove that the following statement is valid.
$$
(s<t \text{ and } t<u)\implies(s<u)
$$
I need to do this assignment using the laws and definitions of inequality.
The problem is that I don't know how to do it.
Can somebody point me in the right direction, how to use the laws and definitions, to solve this.
I am NOT asking from you to solve this for me, I am just asking you, to give me some reference so I can do this on my own.
Thank you very much!

Maybe you could use something like the following: If there exists a number between $a$ and $b$, then either $a < b$ or $b < a$. Use this fact along with the given inequalities to show that only one of these two cases is possible. 
