reserve U for Universe;
reserve x for Element of U;
reserve U1,U2 for Universe;

theorem Th56:
  for A being Category
  for a being Object of A holds [[id a,id a],id a] in the Comp of A
  proof
    let A be Category;
    let a be Object of A;
A1: dom id a = a;
A2: cod id a = a;
    then
A3: [id a,id a] in dom the Comp of A by A1,CAT_1:15;
    (id a)(*)(id a) = id a by A1,CAT_1:22;
    then (the Comp of A).(id a,id a) = id a by A1,A2,CAT_1:16;
    hence thesis by A3,FUNCT_1:def 2;
end;
