reserve A for set;
reserve X,Y,Z for set,x,x1,x2,y,y1,y2,z,z1,z2 for object;

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;
