If target affected by Faerie Fire spell enters an area which is under effect of Darkness, do it lose its effect?

Faerie Fire is 1st level spell and illumintes the target. So, if target affected by Faerie Fire spell enters an area which is under effect of Darkness, do it lose its effect or it dispels the spell entirely? Because Darkness can dispel lower level light spells?

— Gökmen ÖNCÜ (@gman_go) January 5, 2018

The darkness spell dispels light spells in its area that are of 2nd level or lower. For example, faerie fire is a light-producing spell of 1st level. If you are under the effect of faerie fire and enter the area of the darkness spell, faerie fire is dispelled on you. #DnD https://t.co/uDKzn4WDie

— Jeremy Crawford (@JeremyECrawford) January 5, 2018