  Let f : (M,p)\to (M',p') be a formal (holomorphic) nondegenerate map, i.e.
with formal holomorphic Jacobian J_f not identically vanishing, between two
germs of real analytic generic submanifolds in \C^n, p'=f(p). Assuming the
target manifold to be real algebraic, and the source manifold to be minimal at
p\in M in the sense of Tumanov, we prove the convergence of the so-called
reflection mapping associated to f. From this, we deduce the convergence of
such mappings from minimal real analytic generic submanifolds onto real
algebraic holomorphically nondegenerate ones, as well as related results on
partial convergence of such maps. For the proofs, we establish a principle of
analyticity for formal CR power series. This principle can be used to reobtain
the convergence of formal mappings between real analytic CR manifolds under a
standard nondegeneracy condition.
