  We give a short proof for the fact, already proven by Thomas Haettel, that
the arbitrary intersection of parabolic subgroups in Euclidean Braid groups
$A[\tilde{A}_n]$ is again a parabolic subgroup. To that end, we use that the
spherical-type Artin group $A[B_{n+1}]$ is isomorphic to $A[\tilde{A}_n]
\rtimes \mathbb{Z}$.
