Affine spaces/Affine mapping/Affine subspaces/Exercise

Let

$\varphi \colon E\longrightarrow F$

be an affine-linear mapping between the affine spaces ${}E$ and ${}F$ over ${}K$. Show that, for every affine subspace ${}G\subseteq F$, the preimage ${}\varphi ^{-1}(G)$ is an affine subspace of ${}E$.

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