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 Th37:
  for f being Function st f is one-to-one holds <:f,X,Y:> is one-to-one
proof
  let f be Function;
  assume f is one-to-one;
  then Y|`f is one-to-one by FUNCT_1:58;
  hence thesis by FUNCT_1:52;
end;
