Often we want to prove universal statements, perhaps of the form \(\forall x (P(x) \imp Q(x))\text{.}\) Again, we will want to assume \(P(x)\) is true and deduce \(Q(x)\text{.}\) But what about the \(x\text{?}\) We want this to work for all \(x\text{.}\) We accomplish this by fixing \(x\) to be an arbitrary element (of the sort we are interested in).
in-context