reserve C for category,
  o1, o2, o3 for Object of C;

theorem
  for m, m9 being Morphism of o1, o2 st m is _zero & m9 is _zero & ex O
  being Object of C st O is _zero holds m = m9
proof
  let m, m9 be Morphism of o1, o2 such that
A1: m is _zero and
A2: m9 is _zero;
  given O being Object of C such that
A3: O is _zero;
  set n = the Morphism of O, O;
  set b = the Morphism of O, o2;
  set a = the Morphism of o1, O;
  thus m = b * (n" * n) * a by A1,A3
    .= m9 by A2,A3;
end;
