 reserve G for Group;
 reserve H for Subgroup of G;
 reserve a, b, c, x, y for Element of G;
 reserve h for Homomorphism of G, G;
 reserve q, q1 for set;

theorem Th15:
  id the carrier of G is Element of InnAut G
proof
  set I = id the carrier of G;
A1: ex a st for x holds I.x = x |^ a
  proof
    take a = 1_G;
    let x;
A2: a" = 1_G by GROUP_1:8;
    thus I.x = x
      .= x * a by GROUP_1:def 4
      .= x |^ a by A2,GROUP_1:def 4;
  end;
  I is Element of Funcs (the carrier of G, the carrier of G) by FUNCT_2:8;
  hence thesis by A1,Def4;
end;
