Is any morphism from an affine scheme to arbitrary scheme is separated?

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It seems to me that $X \rightarrow Y$ with $X$ affine is separated. Since we have the composition $X \rightarrow Y \rightarrow \mathrm{Spec}\mathbb{Z}$ is a morphism between affine schemes hence separated. But I never ever see anyone talking about this simple result. The common one is a morphism between affine schemes is separated.