reserve B,C,D,C9,D9 for Category;
reserve E for Subcategory of C;

theorem Th24:
  for f,f9 being Morphism of C for g,g9 being Morphism of D st dom
  [f9,g9] = cod [f,g] holds [f9,g9](*)[f,g] = [f9(*)f,g9(*)g]
proof
  let f,f9 be Morphism of C;
  let g,g9 be Morphism of D such that
A1: dom [f9,g9] = cod [f,g];
  [dom f9,dom g9] = dom [f9,g9] & cod [f,g] = [cod f,cod g] by Th22;
  then dom f9 = cod f & dom g9 = cod g by A1,XTUPLE_0:1;
  hence thesis by Th23;
end;
