# Why homotopic equivalence is equivalent to quasi iso in K(I)

Let $$X,Y \in K(A)$$ where $$A$$ is an abelian category and $$X,Y$$ are complexes s.t. $$X^i$$ and $$Y^i$$ are injecive for every i. How can I prove that if $$t : X \to Y$$ is a quasi-isomorphism he $$t$$ is an homotopy equivalence?

Thanks for the references!