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:] = {} & [:f,{}:] = {}
proof
  let f be Function;
  dom [:{},f:] = [:dom {},dom f:] & dom [:f,{}:] = [:dom f,dom {}:] by
FUNCT_3:def 8;
  hence thesis by ZFMISC_1:90;
end;
