reserve x,y for set;
reserve C,C9,D,D9,E for non empty set;
reserve c for Element of C;
reserve c9 for Element of C9;
reserve d,d1,d2,d3,d4,e for Element of D;
reserve d9 for Element of D9;

theorem
  for F being Function holds F[:]({},x) = {}
proof
  let F be Function;
  F[:]({},x) = F.:({}, dom {} --> x);
  hence thesis by Th3;
end;
