$f_n \rightharpoonup f$ in $L^q(Q)$ $\forall q < \infty$ and $f_n' \rightharpoonup f'$ in $L^2(0,T;H^{-1})$ implies $f_n \to f$

Question

(... in $C^0([0,T]; H^{-1})$. )

Let $f_n$ be a sequence of functions defined on $Q:=(0,T)\times \Omega$, where $\Omega$ is a bounded domain.

I have read this:

Since $f_n \rightharpoonup f$ in $L^q(Q)$ for every $q < \infty$ and $f_n' \rightharpoonup f'$ in $L^2(0,T;H^{-1}(\Omega))$, using Aubin's lemma we deduce that $f_n \to f$ in $C^0([0,T]; H^{-1}(\Omega))$.

Can I get a reference to this lemma? It isn't the Lions-Aubin result I don't think.

Source is this paper on page 426.