Extensible implies normal

Statement
Every extensible automorphism of a group is a normal automorphism: it sends every normal subgroup of the group to itself.

Related facts

 * Inner implies extensible
 * Extensible implies subgroup-conjugating
 * Finite-extensible implies class-preserving
 * Extensible automorphism-invariant equals normal

Facts used

 * 1) uses::Extensible implies subgroup-conjugating
 * 2) uses::Subgroup-conjugating implies normal

Proof
The proof follows directly by piecing together facts (1) and (2).