Definition of "nevertheless"

Now no chaſtening for the preſent ſeemeth to be ioyous, but grieuous: neuertheleſſe, afterward it yeeldeth the peaceable fruite of righteouſneſſe, vnto them which are exerciſed thereby.

1611, The Holy Bible, […] (King James Version), London: […] Robert Barker, […], Hebrews 12:11, column 2

Nevertheless, it is clear that the global energy demand for air-conditioning will grow substantially as nations become more affluent, with the consequences of climate change potentially accelerating the demand.

2013 September-October, Michael Sivak, “Will AC Put a Chill on the Global Energy Supply?”, in American Scientist