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

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.