  In this article we prove that for any saturated fusion system, that the
(unique) smallest weakly normal subsystem of it on a given strongly closed
subgroup is actually normal. This has a variety of corollaries, such as the
statement that the notion of a simple fusion system is independent of whether
one uses weakly normal or normal subsystems. We also develop a theory of weakly
normal maps, consider intersections and products of weakly normal subsystems,
and the hypercentre of a fusion system.
