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We consider the holographic dual of four-dimensional QCD in type IIA supergravity based on the D4-D8-D8-bar model. We show that two recently discovered generalised anomalies are naturally recovered by reduction of the topological couplings in the bulk supergravity action on the internal space. In particular, we give a bulk derivation of the anomaly, first computed by Tanizaki , between the discrete axial symmetry and the diagonal component of the flavour symmetry. We further give a bulk derivation of the anomaly between the periodicity of theta and the flavour symmetry in massive QCD, and find agreement with the results of Cordova, Freed, Lam, and Seiberg.