The given relation is:
$emp(empid, speciality, managerid)$
The following functional dependencies hold:
$managerid \to speciality $
$empid,speciality \to managerid$
Thus, we see that (empid, speciality) is the candidate key.
Thus, the relation is in 3NF as the RHS of first dependency is prime attribute while the LHS of the second dependency is the superkey.