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

theorem
  for A, B being category, F being contravariant Functor of A, B for o1,
  o2 being Object of A st o1, o2 are_iso holds F.o2, F.o1 are_iso
proof
  let A, B be category, F be contravariant Functor of A, B, o1, o2 be Object
  of A;
  assume
A1: o1, o2 are_iso;
  then consider a being Morphism of o1, o2 such that
A2: a is iso;
A3: <^o1,o2^> <> {} & <^o2,o1^> <> {} by A1;
  hence <^F.o2,F.o1^> <> {} & <^F.o1,F.o2^> <> {} by FUNCTOR0:def 19;
  take F.a;
  thus thesis by A3,A2,Th24;
end;
