  We give a lower bound on the ground state energy of a system of two fermions
of one species interacting with two fermions of another species via point
interactions. We show that there is a critical mass ratio m_c \approx 0.58 such
that the system is stable, i.e., the energy is bounded from below, for m \in
[m_c, m_c^{-1}]. So far it was not known whether this 2+2 system exhibits a
stable region at all or whether the formation of four-body bound states causes
an unbounded spectrum for all mass ratios, similar to the Thomas effect. Our
result gives further evidence for the stability of the more general N+M system.
