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 Th16:
  for g,f being GroupMorphism st dom(g) = cod(f) ex G1,G2,G3 being
  AddGroup st g is Morphism of G2,G3 & f is Morphism of G1,G2
proof
  defpred P[GroupMorphism,GroupMorphism] means dom($1) = cod($2);
  let g,f be GroupMorphism such that
A1: P[g,f];
  consider G2,G3 being AddGroup such that
A2: g is Morphism of G2,G3 by Th14;
  consider G1,G29 being AddGroup such that
A3: f is Morphism of G1,G29 by Th14;
A4: G29 = cod(f) by A3,Def12;
  G2 = dom(g) by A2,Def12;
  hence thesis by A1,A2,A3,A4;
end;
