
theorem Th48:
  for C1,C2 being category holds
  C1 [x] C2,pr1(C1,C2),pr2(C1,C2) is_product_of C1,C2
  proof
    let C1,C2 be category;
    set T = the categorical_product of C1,C2;
    consider D be strict category, P1 be Functor of D,C1,
    P2 be Functor of D,C2 such that
A1: T = [D,P1,P2] & P1 is covariant & P2 is covariant &
    D,P1,P2 is_product_of C1,C2 by Def18;
    thus thesis by A1;
end;
