reserve x,x1,x2,y,y9,y1,y2,z,z1,z2 for object,P,X,X1,X2,Y,Y1,Y2,V,Z for set;

theorem
  for f being PartFunc of X,Y st (for x1,x2 being Element of X st x1 in
  dom f & x2 in dom f & f.x1 = f.x2 holds x1 = x2) holds f is one-to-one;
