Corollary 5

Let u : C \to C' be a homologism of complexes of right a-modules, flat and bounded on the right. For every complex E of left a-modules, the morphism $u \otimes 1_E : C \otimes_A E \to C' \otimes_A E$ is a homologism.

Indeed, Con (u) is a flat complex, bounded on the right and of zero homology; then one has H(Con (u) \otimes_A E) = 0 by cor. 4, hence H(Con (u \otimes 1_E)) = 0 (X, p. 67, lemma 2), and $u \otimes 1_E$ is a homologism.