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 y in f.:X ex x being Element of X st x
  in dom f & y = f.x
proof
  let f be PartFunc of X,Y;
  assume y in f.:X;
  then ex x being object st x in dom f & x in X & y = f.x by FUNCT_1:def 6;
  hence thesis;
end;
