Is Java's TimeZone thread-safe?

I wanted my application to just have one TimeZone object which will be used by many SimpleDateFormat and Calendar objects from the other places concurrently. This is to avoid having to always do TimeZone.getTimeZone(ID).

I know SimpleDateFormat and Calendar classes are not thread safe, which is why I configure one thread to always create new instances of them. But what about TimeZone? It is not clear to me whether I can do the following safely:

final TimeZone tz = TimeZone.getTimeZone("GMT");
...
//Thread 1.
Thread t1 = new Thread(Runnable(){
    public void run()
    {
        Calendar cal = Calendar.getInstance(tz);
        ...
        SimpleDateFormat sdf = new SimpleDateFormat();
        sdf.setTimeZone(tz);
        ...
    }
});
t1.start();
...
//Thread 2.
Thread t2 = new Thread(Runnable(){
    public void run()
    {
        Calendar cal = Calendar.getInstance(tz);
        ...
        SimpleDateFormat sdf = new SimpleDateFormat();
        sdf.setTimeZone(tz);
        ...
    }
});
t2.start();
...

Thanks!