  For an arbitrary partially ordered set $P$ its {\em dual} $P^*$ is built as
the collection of all monotone mappings $P\to\2$ where $\2=\{0,1\}$ with $0<1$.
The set of mappings $P^*$ is proved to be a complete lattice with respect to
the pointwise partial order. The {\em second dual} $P^{**}$ is built as the
collection of all morphisms of complete lattices $P^*\to\2$ preserving
universal bounds. Then it is proved that the partially ordered sets $P$ and
$P^{**}$ are isomorphic.
