reserve x, y for set;
reserve D for non empty set;
reserve UN for Universe;
reserve C for Category;
reserve O for non empty Subset of the carrier of C;
reserve G,H for AddGroup;

theorem Th22:
  for f,g,h being strict GroupMorphism st dom h = cod g & dom g =
  cod f holds h*(g*f) = (h*g)*f
proof
  let f,g,h be strict GroupMorphism such that
A1: dom h = cod g and
A2: dom g = cod f;
  set G2 = cod f, G3 = cod g;
  reconsider h9 = h as Morphism of G3,(cod h) by A1,Def12;
  reconsider g9 = g as Morphism of G2,G3 by A2,Def12;
  reconsider f9 = f as Morphism of (dom f),G2 by Def12;
  h9*(g9*f9) = (h9*g9)*f9 by Th21;
  hence thesis;
end;
