Recently, Nies, Segal and Tent started investigating finite axiomatizability in the realm of profinite groups. Among the profinite groups they consider is the class of p-adic analytic pro-p groups, whose rank they characterize by a single first-order sentence up to a certain error term. In joint work with Benjamin Klopsch we show that not only the rank, but also the dimension of these groups can be fully characterized by a single first-order sentence. Actually, this even turns out to be true for so-called pro-pi groups. No familiarity with p-adic analytic pro-p groups (or pro-pi groups) will be assumed.