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

theorem
  for f being Morphism of o1, o2, g, h being Morphism of o2, o1 st h * f
  = idm o1 & f * g = idm o2 & <^o1,o2^> <> {} & <^o2,o1^> <> {} holds g = h
proof
  let f be Morphism of o1, o2, g, h be Morphism of o2, o1 such that
A1: h * f = idm o1 and
A2: f * g = idm o2 & <^o1,o2^> <> {} and
A3: <^o2,o1^> <> {};
  thus g = h * f * g by A1,A3,ALTCAT_1:20
    .= h * idm o2 by A2,A3,ALTCAT_1:21
    .= h by A3,ALTCAT_1:def 17;
end;
