Washing meat spoon used for DE pareve desert in meat dishwasher

Question:

After our meat meal, we cleared table and brought out pareve DE ice cream. We served ice cream with a meat spoon. Then we put the meat serving spoon in dishwasher and washed it with meat dishes. Is this permitted? Or is the dishwasher considered like a cooking utensil and the spoon would need to be washed separately?

Answer:

The spoon may be washed with the other meat dishes. The reason is because DE only means that the equipment was originally used for dairy, however in retrospect it will not prohibit anythig if it was used with meat. This is because, any absorbed taste was a nat bar nat, (doubly absorbed taste) of kosher food, and it will not make anything ttrief.