(Contravariant) Koszul duality for DG algebras

A DG algebras $A$ over a field $k$ with $H(A)$ connected and $H_{<0}(A)=0$ has a unique up to isomorphism DG module $K$ with $H(K)\cong k$. It is proved that if $H(A)$ is degreewise finite, then $RHom_A(?,K): D^{df}{+}(A)^{op} \equiv D{df}^{+}}(RHom_A(K,K))$ is an exact equivalence of derived categories of DG modules with degreewise finite-dimensional homology. It induces an equivalences of $D_b^{df}(A{)}^{op}$ and the category of perfect DG $RHo{m}_A(K,K)$-modules, and vice-versa. Corresponding statements are proved also when $H(A)$ is simply connected and $H^{<0}(A)=0$.