Let x and y be strings and let L be any language. We say that x and y are distinguishable by L if some string z exists whereby exactly one of the strings xz and yz is a member of L; otherwise, for every string z, $xz \in L$ whenever $yz \in L$ and we say that x and y are indistinguishable by L. If x an y are indistinguishable by L we write $x \equiv_L y$. Show that $\equiv_L$ is an equivalence relation.
It seems quite obvious to me, it is reflexive, symmetric and transitive. I have no idea as to how should I write a formal proof. I'd appreciate some help.