Unlinkability is a privacy property of crucial importance for several systems such as mobile phones or RFID chips. Analysing this security property is very complex, and highly error-prone. Therefore, formal verification with machine support is desirable. Unfortunately, existing techniques are not sufficient to directly apply verification tools to automatically prove unlinkability. In this paper, we overcome this limitation by defining a simple. transformation that will exploit several features recently introduced in the tool ProVerif. This transformation, together with some generic axioms, allow the tool to successfully conclude on several case studies. We have implemented our approach, effectively obtaining direct proofs of unlinkability on several protocols that were, until now, out of reach of automatic verification tools. Moreover, our approach is not specific to unlinkability and could, in principle, be useful in other contexts.