Definability of Forcing

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I am studying Kunen's Set Theory and in the section where the atomic definability lemma is discussed, it just says the notion $p\Vdash^* \phi$, where $\phi$ is atomic, is obviously definable over $M$. The problem is that it doesn't mention an explicit $\{\in \}$- formula that defines the atomic formula. Can anyone help me understand it or actually give a proof of it?