  We generalize methods, developed by S. Ghilardi, and apply them to a
subsystem J$_2$ of bimodal provability logic GLB. We describe projective
formulas in J$_2$ in terms of Kripke semantics and prove that logic J$_2$ has
finitary unification type. As an application, we show that admissibility
problem for J$_2$ is decidable.
