Lemma 15.95.3. Let $A$ be a ring and let $f \in A$ be a nonzerodivisor. If $M^\bullet \to N^\bullet $ is a quasi-isomorphism of complexes of $f$-torsion free $A$-modules, then the induced map $\eta _ fM^\bullet \to \eta _ fN^\bullet $ is a quasi-isomorphism too.

**Proof.**
This is true because the isomorphisms of Lemma 15.95.2 are compatible with maps of complexes.
$\square$

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