reserve v,x,x1,x2,y,z for object,
  X,X1,X2,X3 for set;

theorem Th5:
  for X,Y,Z be non empty set
  ex I be Function of [:X,Y,Z:],product <*X,Y,Z*>
  st I is one-to-one & I is onto
  & for x,y,z be object st x in X & y in Y & z in Z
     holds I.(x,y,z) = <*x,y,z*>
  proof
    let X,Y,Z be non empty set;
    dom <*X,Y,Z*> = {1,2,3} & <*X,Y,Z*>.1 = X
     & <*X,Y,Z*>.2 = Y & <*X,Y,Z*>.3 = Z by FINSEQ_1:89,FINSEQ_3:1;
    hence thesis by Th4;
  end;
