TITLE: Characterization of right properness using slice categories
QUESTION [5 upvotes]: I would like to know how to cite this theorem (which has a quite surprising consequence):

A model category $\mathcal{M}$ is right proper if and only if for any
  weak equivalence $f:A\to B$, the Quillen adjunction
  $\Sigma_f:\mathcal{M}/ A \leftrightarrows \mathcal{M} / B:f^*$ is a Quillen equivalence.

I had never heard of it (I never read that in any textbook I believe) before I browse the nLab site which refers to this blog comment from C. Rezk.

REPLY [4 votes]: This is Proposition 2.7 in Rezk's Every Homotopy Theory of Simplicial Algebras Admits a Proper Model