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
  PFuncs({},Y) = { {} }
proof
  for x be object holds x in PFuncs({},Y) iff x = {}
  proof
    let x be object;
    thus x in PFuncs({},Y) implies x = {}
    proof
      assume x in PFuncs({},Y);
      then x is PartFunc of {},Y by Th46;
      hence thesis;
    end;
    {} is PartFunc of {},Y by RELSET_1:12;
    hence thesis by Th45;
  end;
  hence thesis by TARSKI:def 1;
end;
