Wilkie (1999) proved that the structure generated by all real Pfaffian functions is o-minimal.Subsequently Speissegger (1999) proved the o-minimality of the Pfaffian closure of an o-minimal structure. We give an alternative proof of this theorem. Moreover our result holds not only over the real numbers but more generally for definably complete Baire structures, which we introduced in 2008 and which form an axiomatizable class.