I've got a class with several properties. On every value update, a Store method is called with stores all fields (in a file).

private int _Prop1;
public int Prop1 {
    get {
        return _Prop1;
    }
    set {
        _Prop1 = value;
        Store();
    }
}

// more similar properties here...

private XmlSerializer _Ser = new ...;
private void Store()
{
    lock (_Ser) {
        using (FileStream fs = new ...) {
            _Ser.Serialize (fs, this);
        }
    }
}

Is this design thread-safe?

(Btw, if you can think of a more appropriate caption, feel free to edit.)