  The well known Boole-Shannon expansion of Boolean functions in several
variables (with co-efficients in a Boolean algebra $B$) is also known in more
general form in terms of expansion in a set $\Phi$ of orthonormal functions.
However, unlike the one variable step of this expansion an analogous
elimination theorem and consistency is not well known. This article proves such
an elimination theorem for a special class of Boolean functions denoted
$B(\Phi)$. When the orthonormal set $\Phi$ is of polynomial size in number $n$
of variables, the consistency of a Boolean equation $f=0$ can be determined in
polynomial number of $B$-operations. A characterization of $B(\Phi)$ is also
shown and an elimination based procedure for computing consistency of Boolean
equations is proposed.
