reserve X for set;
reserve UN for Universe;

theorem
  for A,B being non empty set st [:A,B:] is Element of UN holds
  A is Element of UN & B is Element of UN
  proof
    let A,B be non empty set;
    assume
A1: [:A,B:] is Element of UN;
    proj1 [:A,B:] = A & proj2 [:A,B:] = B by FUNCT_5:9;
    hence thesis by A1,Th36;
 end;
