I do not know how to ask my question properly but please allow me to state it. I want to express this claim in logical notation. "For all integers a,b,c if a|b and b|c then a|c."
The logical notation involves things like $\implies$, $\vee$, $\wedge$, $\forall$, and so on.
If the sign $|$ is allowed: $$\forall a\forall b\forall c((a|b\land b|c)\implies a|c).$$