Is `std::move` necessary here?

Is std::move necessary in the following snippet?

std::function<void(int)> my_std_function;

void call(std::function<void(int)>&& other_function)
{
  my_std_function.swap(std::move(other_function));
}

As far as I know call() accepts a rvalue reference.. but since the rvalue reference is itself an lvalue, in order to call swap(std::function<void(int)>&&) I have to re-cast this to an rvalue reference with std::move

Is my reasoning correct or std::move can be omitted in this case (and if it can, why?)