We prove that lattice QCD generates the axial anomaly in the continuum limi
t under very general conditions on the lattice action, which includes the c
ase of Ginsparg-Wilson fermions. The ingredients going into the proof are g
auge invariance, locality of the Dirac operator, absence of fermion doubtin
g, the general form of the lattice Ward identity, and the power counting th
eorem of Reisz. The results generalize in an obvious way to SU(N) lattice g
auge theories.