  Three dimensional bosonization is a conjectured duality between
non-supersymmetric Chern-Simons theories coupled to matter fields in the
fundamental representation of the gauge group. There is a well-established
supersymmetric version of this duality, which involves Chern-Simons theories
with ${\cal N} = 2$ supersymmetry coupled to fundamental chiral multiplets.
Assuming that the supersymmetric duality is valid, we prove that
non-supersymmetric bosonization holds for all planar correlators of
single-trace operators. The main tool we employ is a double-trace flow from the
supersymmetric theory to an IR fixed point, in which the scalars and fermions
are effectively decoupled in the planar limit. A generalization of this
technique can be used to derive the duality mapping of all renormalizable
couplings, in non-supersymmetric theories with both a scalar and a fermion. Our
results do not rely on an explicit computation of planar diagrams.
