Affine Group of One Dimension is Group/Proof 2

Theorem

Let $\map {\operatorname {Af}_1} \R$ be the $1$-dimensional affine group on $\R$.

Then $\map {\operatorname {Af}_1} \R$ is a group.

Proof

It follows from Affine Group of One Dimension as Semidirect Product and Semidirect Product of Groups is Group.

$\blacksquare$