I would say that is all he probably needs as in sleep time. Perhaps when you see he gets 'starey' try some quiet time with books or a movie and that may give you a little bit extra time.
Does he go to bed any earlier? I found when they dropped that 2nd sleep they went down much easier at night and a bit earlier until they wanted to drop the day sleep and still slept and became very difficult to put down out night (hope that made sense?).
It made no difference though to the time they get up though whatever was happening sleep during the day