Are phenols good antioxidants?
Phenolic compounds, or in general aromatics actually, has electrons which many oxidants can easily abstract or bind to molecule. 

http://www.springer.com/cda/content/document/cda_downloaddocument/9781441978257-c1.pdf?SGWID=0-0-45-1106848-p174056970

From the above link in page 17,


as you see the highest rates, order of magnitude or even more higher ones come from aromatics, or at least pi-bond between carbons. It can reasonably assumed that if you have these compounds in a mixture, the possibility of any oxidant introduced reacts with them is higher than the other ones. In short, they are good anti-oxidants in that way.