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

theorem Th22:
  for f being Morphism of C for g being Morphism of D
   holds dom [f,g] = [dom f,dom g] & cod [f,g] = [cod f,cod g]
proof
  let f be Morphism of C;
  let g be Morphism of D;
  thus dom [f,g] = [:the Source of C,the Source of D:].(f,g)
    .= [dom f,dom g] by FUNCT_3:75;
  thus cod [f,g] = [:the Target of C,the Target of D:].(f,g)
    .= [cod f,cod g] by FUNCT_3:75;
end;
