  The aim of the present note is to show that the natural map from classical
braids to virtual braids is an inclusion; this proof does not use any complete
invariants of classical braids; it is based on the projection from virutal
braids to classical braids (similar to the one given in \cite{Projection});
this projection is the idenitiy map on the set of virtual braids. The
projection is well defined not only for the virtual braid group but also for
the quotient group of the virtual (pure) braid group by the so-called
virtualization move. The idea of this projection is closely related to the
notion of parity and to the groups $G_{n}^{k}$, introduced by the author.
