
theorem Th51:
  for C1,C2 being category holds id C1 [x] id C2 = id(C1 [x] C2)
  proof
    let C1,C2 be category;
A1: (id C1)(*)pr1(C1,C2) = pr1(C1,C2) by CAT_7:11
    .= pr1(C1,C2)(*)id(C1 [x] C2) by CAT_7:11;
    (id C2)(*)pr2(C1,C2) = pr2(C1,C2) by CAT_7:11
    .= pr2(C1,C2)(*)id(C1 [x] C2) by CAT_7:11;
    hence id C1 [x] id C2 = id(C1 [x] C2) by A1,Def22;
  end;
