reserve x, y for object, X, X1, X2 for set;
reserve Y, Y1, Y2 for complex-functions-membered set,
  c, c1, c2 for Complex,
  f for PartFunc of X,Y,
  f1 for PartFunc of X1,Y1,
  f2 for PartFunc of X2, Y2,
  g, h, k for complex-valued Function;

theorem
  <-><->f = f
proof
  set f1 = <->f;
A1: dom f1 = dom f by Def33;
  hence
A2: dom<->f1 = dom f by Def33;
  let x be object;
  assume
A3: x in dom<->f1;
  hence (<->f1).x = -f1.x by Def33
    .= -(-f.x) by A1,A2,A3,Def33
    .= f.x;
end;
