  We present a derivation of the holographic dual of logarithmic negativity in
AdS$_3$/CFT$_2$ that was recently conjectured in [Phys. Rev. D 99, 106014
(2019)]. This is given by the area of an extremal cosmic brane that terminates
on the boundary of the entanglement wedge. The derivation consists of relating
the recently introduced R\'enyi reflected entropy to the logarithmic negativity
in holographic conformal field theories. Furthermore, we clarify previously
mysterious aspects of negativity at large central charge seen in conformal
blocks and comment on generalizations to generic dimensions, dynamical
settings, and quantum corrections.
