How can Albert - from the fact that Bernard a) has knowledge of the day and b) eliminated May and June as valid options the month value - deduce the correct date himself? I.e. if Bernard was given the day 17, he still would known the correct date (August 17 in this case)

But Albert can't know that. From his point of view, even if Bernard knows the correct date, he still has three valid options to consider: July 16, August 15 and August 17.

So how can he know the correct date?