  In 1964 Vizing proved that starting from any k-edge-coloring of a graph G one
can reach, using only Kempe swaps, a ($\Delta$ + 1)-edge-coloring of G where
$\Delta$ is the maximum degree of G. One year later he conjectured that one can
also reach a $\Delta$-edge-coloring of G if there exists one. Bonamy et. al
proved that the conjecture is true for the case of triangle-free graphs. In
this paper we prove the conjecture for all graphs.
