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

theorem Th3:
  for m being Morphism of o1, o2 st <^o1,o2^> <> {} & <^o2,o1^> <>
  {} & m is iso holds m" is iso
proof
  let m be Morphism of o1, o2 such that
A1: <^o1,o2^> <> {} & <^o2,o1^> <> {};
  assume m is iso;
  then
A2: m is retraction coretraction by ALTCAT_3:5;
  hence m"*(m")" = m" * m by A1,ALTCAT_3:3
    .= idm o1 by A1,A2,ALTCAT_3:2;
  thus (m")"*m" = m * m" by A1,A2,ALTCAT_3:3
    .= idm o2 by A1,A2,ALTCAT_3:2;
end;
