theorem
  for f1,f2 being Function of [:X,Y:],Z st for a being Element of X for
  b being Element of Y holds f1.(a,b) = f2.(a,b) holds f1 = f2
proof
  let f1,f2 be Function of [:X,Y:],Z;
  assume
  for a being Element of X for b being Element of Y holds f1.(a,b) = f2.(a,b);
  then for x,y being set st x in X & y in Y holds f1.(x,y) = f2.(x,y);
  hence thesis by Th1;
end;
