Pumping is Breastfeeding

Is it?

Yes it is, but you are forgetting the designer aspect of breast milk so try to nurse at least once per day to make that designer milk. What is designer milk? When the baby is exposed to germs, her saliva has antigens to those germs and your body will create antibodies for those germs via your designer breastmilk. This exchange of antibodies and antigens is a very simplified example of the magic that happens with nursing at the breast. 

So Yes, pumping is offering breast milk, but try to also add in nursing at the breast (even if it's one or two nursing times per day) for that specific designer breast milk your baby is needing!