  Let $\mathbf{K}$ be an algebraically closed field of arbitrary
characteristic, complete with respect to a non-archimedean absolute value
$|\,|$. We establish a Second Main Theorem type estimate for analytic map
$f\colon \mathbf{K}\rightarrow\mathbb{P}^n(\mathbf{K})$ and a family of $n$
hypersurfaces in $\mathbb{P}^n(\mathbf{K})$ intersecting transversally and not
all being hyperplanes. This implements the previous work of Levin where the
case of all hypersurfaces having degree greater than one was studied.
