Divisibility relation: transitivity proof !Proof I'm a bit confused about the proof for this relation. I get the first part, but the second line is where I'm totally muffled! Any help is greatly appreciated :) ** An example would also be helpful

You wish to show that $c\mid(ma+nb)$, in other words, there exists a $k$ such that $ma+nb=ck$. This is exactly what the second line does, it shows that $ma+nb=c(me+nf)$.