Though, If he eats dairy, then he is not a vegan.
There are many kinds of vegetarianism.
Lacto-ovo vegetarian - Eats dairy. Eats eggs. No meat of any kind.
Ovo vegetarian - Eats eggs. No dairy of any kind. No meat of any kind.
Lacto vegetarian - Eats dairy. No eggs. No meat of any kind.
Vegan vegetarian - Strictest form of vegetarianism. Only fruits, vegetables, whole grains (nothing processed), seeds, nuts and legumes.