  We reconsider the Adler-Bardeen theorem for the cancellation of gauge
anomalies to all orders, when they vanish at one loop. Using the
Batalin-Vilkovisky formalism and combining the dimensional-regularization
technique with the higher-derivative gauge invariant regularization, we prove
the theorem in the most general perturbatively unitary renormalizable gauge
theories coupled to matter in four dimensions, and identify the subtraction
scheme where anomaly cancellation to all orders is manifest, namely no
subtractions of finite local counterterms are required from two loops onwards.
Our approach is based on an order-by-order analysis of renormalization, and,
differently from most derivations existing in the literature, does not make use
of arguments based on the properties of the renormalization group. As a
consequence, the proof we give also applies to conformal field theories and
finite theories.
