A From two-body Green's function to one-body in perturbation theory

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Hi guys! I am trying to derive the Hedin's equations used for GW on my own, and I found this equation, but I cannot really derive it, nor find a source where they explain how this can be derived (they link to other papers that in the end don't show where this is coming from). The equation I am talking about is:
$$G(1,3,2,3^+) = G(1,2)G(3,3^+)-\frac{\delta G(1,2)}{\delta \phi(3)}$$
Can somebody tell me how this can be derived or just link me to a document with a full derivation?
Thanks!
 
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