Could someone point me toward a proof that "ZF + AD + every set of reals is Suslin" (+ $\mathsf{DC}\_\mathbb{R}$?) implies $\mathsf{AD}\_\mathbb{R}$, either with a reference or a hint?

I am interested how local the proof is; that is, which sets of reals need to be Suslin in order to show the determinacy of a particular real game.