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