  We investigate in 4 spacetime dimensions, all the consistent deformations of
the lagrangian ${\cal L}_2+{\cal L}_{{3/2}}$, which is the sum of the
Pauli-Fierz lagrangian ${\cal L}_2$ for a free massless spin 2 field and the
Rarita-Schwinger lagrangian ${\cal L}_{{3/2}}$ for a free massless spin 3/2
field. Using BRST cohomogical techniques, we show, under the assumptions of
locality, Poincar\'e invariance, conservation of the number of gauge symmetries
and the number of derivatives on each fields, that N=1 D=4 supergravity is the
only consistent interaction between a massless spin 2 and a massless spin 3/2
field. We do not assume general covariance. This follows automatically, as does
supersymmetry invariance. Various cohomologies related to conservations laws
are also given.
