Traveling to Shanghai to Beijing then to Hong Kong

We have a whole Asian trip planned. We have tickets booked from Manila to Shanghai, staying one night in Shanghai (6/26), leaving for Beijing the next day (6/27) and staying 2 nights (6/27 & 6/28) before departing for Hong Kong on 6/29. We are not going back to Shanghai before leaving mainland China. Do we qualify for the 72-hour visa-free policy? We definitely fall within the 72 hours but we are not flying out of the same City we flew into. Please advise. Thank you!