The closed form integral representation for the projection onto the subspace spanned by bound states of the two-body Coulomb Hamiltonian is obtained. The projection operator onto the n²-dimensional subspace corresponding to the nth eigenvalue in the Coulomb discrete spectrum is also represented as the combination of Laguerre polynomials of nth and (n - 1)th order. The latter allows us to derive an analogue of the Christoffel-Darboux summation formula for the Laguerre polynomials. The representations obtained are believed to be helpful in solving the breakup problem in a system of three charged particles where the correct treatment of infinitely many bound states in two-body subsystems is one of the most difficult technical problems.