reserve X for set;

theorem Th1:
  X = {} or ex a be set st {a} = X or ex a,b be set st a<>b & a in X & b in X
proof
  now
    set p = the Element of X;
    assume X <> {} & not ex a,b be set st a<>b & a in X & b in X;
    then for z be object holds z in X iff z = p;
    then X={p} by TARSKI:def 1;
    hence ex a be set st {a} = X;
  end;
  hence thesis;
end;
