reserve B,C,D for Category;

theorem Th34:
  for S being Contravariant_Functor of C opp,B, c being Object of
  C holds (Obj /*S).c = (Obj S).(c opp)
proof
  let S be Contravariant_Functor of C opp,B, c be Object of C;
A1: now
    let c be Object of C;
    (/*S).(id c) = id((Obj S).(c opp)) by Lm10;
    hence ex d being Object of B st (/*S).(id c) = id d;
  end;
  (/*S).(id c) = id((Obj S).(c opp)) by Lm10;
  hence thesis by A1,CAT_1:66;
end;
