  In a modular approach, we lift Hilbert-style proof systems for propositional,
modal and first-order logic to generalized systems for their respective
team-based extensions. We obtain sound and complete axiomatizations for the
dependence-free fragment FO(~) of V\"a\"an\"anen's first-order team logic TL,
for propositional team logic PTL, quantified propositional team logic QPTL,
modal team logic MTL, and for the corresponding logics of dependence,
independence, inclusion and exclusion.
  As a crucial step in the completeness proof, we show that the above logics
admit, in a particular sense, a semantics-preserving elimination of modalities
and quantifiers from formulas.
