let G be strict Group; :: thesis: id the carrier of G is Element of Aut G
id the carrier of G is Homomorphism of G,G by GROUP_6:38;
then consider h being Homomorphism of G,G such that
A1: h = id the carrier of G ;
rng h = the carrier of G by A1, RELAT_1:45;
then h is onto ;
hence id the carrier of G is Element of Aut G by A1, Def1; :: thesis: verum