 Team logic (Väänänen 2007a,b; Kontinen &amp; Nurmi 2009) extends dependence logic by adding to it a contradictory negation \(\lnot\). It is equi-expressive with full second order logic, both in terms of definability of classes of models (Väänänen 2007b) and with respect to the classes of teams that team logic expressions can define with respect to a given model (Kontinen &amp; Nurmi 2009). In (Lück 2019), a Hilbert-style axiomatization for Team Logic (and for its modal and propositional equivalents) was found that is complete for its dependence-free fragment (that is, for the fragment in which dependence atoms do not appear).