Extensible automorphism-invariant equals normal

Statement
The following are equivalent for a subgroup of a group:


 * The subgroup is a normal subgroup: it is invariant under all inner automorphisms of the whole group.
 * The subgroup is an extensible automorphism-invariant subgroup: it is invariant under all extensible automorphisms of the whole group.

Facts used

 * 1) uses::Inner implies extensible
 * 2) uses::Extensible implies normal