reserve A for set,
  C for non empty set,
  B for Subset of A,
  x for Element of A,
  f,g for Function of A,C;

theorem Th3:
  for B being set holds f +* g|B is Function of A,C
proof
  let B be set;
A1: dom f = A & dom g = A by FUNCT_2:def 1;
  dom (f +* g|B) = dom f \/ dom (g|B) by FUNCT_4:def 1
    .= dom f \/ dom g /\ B by RELAT_1:61
    .= A by A1,XBOOLE_1:22;
  hence thesis by FUNCT_2:67;
end;
