Short answer: consult a qualified professional arborist about any
further trimming these two trees may need.

Longer answer: they will survive, and may do very well, especially
if the cut is directly above the branches. No stump sticking up?
Often the stump will die back to the union (where the branches are)
and the tree will try to cover the stump from the union upward.
Cutting the stump flush with the union helps the tree cover the
wound before significant rot sets in.

Two trees 3 feet apart is not ideal. Consider removing the weaker
one.

Una