theorem
  [:X1,X2:] = the set of all  [x1,x2]
proof
  defpred P[set,set] means not contradiction;
A1: for x being Element of [:X1,X2:] holds x in the set of all  [x1,x2]
  proof
    let x be Element of [:X1,X2:];
    x = [x`1,x`2];
    hence thesis;
  end;
  for X1,X2 holds { [x1,x2] : P[x1,x2] } is Subset of [:X1,X2:] from
  Fraenkel2;
  then the set of all  [x1,x2]  is Subset of [:X1,X2:];
  hence thesis by A1,SUBSET_1:28;
end;
