B737-700 First Officer reports a left engine bleed trip at FL390 that cannot be reset. Flight is able to continue to destination; avoiding icing conditions per the QRH.

Narrative

During cruise at FL390; the number one engine's Bleed Trip Off light illuminated. We followed the QRH and turned off the left pack; as it would not reset. The Captain contacted Dispatch; reported the problem; and asked for icing conditions enroute. Our concern was that we may enter icing conditions; which the QRH cautions to avoid with a Bleed Trip Off light. The weather at destination was reported as two broken cloud layers at 10;000 FT and 20;000 FT; and no reports of icing. Dispatch asked us to attempt an arrival; and gave us a divert alternate if we couldn't avoid icing conditions. Our engine anti-ice was operating normally for both engines and we assumed that the FOM 'icing conditions' of less than one mile visibility and less than ten degrees Celsius was to be applied to the engines; and visible structural ice would be applied to any wing anti-icing limitations. During the descent; we asked each Controller of any reported icing conditions. They reported none; so we continued the arrival maintaining VMC. I think more detail in the QRH about what anti-icing systems are available; and what to do if it is impossible to avoid icing conditions would be a great help.