reserve P,Q,X,Y,Z for set, p,x,x9,x1,x2,y,z for object;
reserve D for non empty set;

theorem Th62:
  for f1,f2 being Function of X,Y st for x being Element of X
  holds f1.x = f2.x holds f1 = f2
proof
  let f1,f2 be Function of X,Y;
  assume for x being Element of X holds f1.x = f2.x;
  then for x being object st x in X holds f1.x = f2.x;
  hence thesis by Th12;
end;
