Extensible implies subgroup-conjugating

Statement
Every extensible automorphism of a group must be a subgroup-conjugating automorphism: it must sned every subgroup to a conjugate subgroup.

Corollaries

 * Extensible implies normal
 * Extensible automorphism-invariant equals normal

Facts used

 * 1) uses::Extensible implies permutation-extensible
 * 2) uses::Equivalence of definitions of subgroup-conjugating automorphism: This essentially shows that the notion of permutation-extensible is equivalent to the notion of subgroup-conjugating.

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