theorem
  H is biconditional implies (M,v |= H iff (M,v |= the_left_side_of H
  iff M,v |= the_right_side_of H))
proof
  assume H is biconditional;
  then H = (the_left_side_of H) <=> (the_right_side_of H) by ZF_LANG:49;
  hence thesis by ZF_MODEL:19;
end;
