Chapter 8.4, Problem 5ES

Prove the transitivity of modular congruence. That is, prove that for all integers $a,b,c,$ and n with $n>1$ , if $a=b\left(\mathrm{mod}n\right)$ and $b=c\left(\mathrm{mod}n\right)$ then $a=c\left(\mathrm{mod}n\right)$ .