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 Th3:
  for F,f being Function holds F.:({},f) = {} & F.:(f,{}) = {}
proof
  let F,f be Function;
  F.:({},f) = F*{} by Th1;
  hence thesis by Th1;
end;
