Board Thread:Arrow discussions/@comment-9346948-20181211010912/@comment-3221148-20181211175651

You could argue that her second quote does mean that Bruce Wayne is Batman, why else would he be proud of... Batwoman. We'll discuss that among the administration. In any case, it will probably be confirmed by the time Batwoman airs.

Meanwhile, we have Bruce Wayne of Earth-38, who is the "frenemy" of Clark Kent, but was never called Batman... only "Vigilante", heh.