  For a fixed Feynman graph one can consider Feynman integrals with all
possible powers of propagators and try to reduce them, by linear relations, to
a finite subset of integrals, the so-called master integrals. Up to now, there
are numerous examples of reduction procedures resulting in a finite number of
master integrals for various families of Feynman integrals. However, up to now
it was just an empirical fact that the reduction procedure results in a finite
number of irreducible integrals. It this paper we prove that the number of
master integrals is always finite.
