  Let $E \rightarrow M$ be a smooth vector bundle with a bilinear product on
$\Gamma(E)$ satisfying the Jacobi identity. Assuming only the existence of an
anchor map $\mathfrak{a}$ we show that $\mathfrak{a}([X,Y]) =
[\mathfrak{a}X,\mathfrak{a}Y]_c$. This gives the redundancy of the homomorphism
condition in the definition of Leibniz algebroid (in particular if it arises
from a Nambu-Poisson manifold); an aspect not addressed in the literature. We
apply our result to the brackets of Hagiwara, Ibanez et. al; we settle an old
query of Uchino on redundancy for Courant bracket.
