The minors of matroids with an adjoint

If $M$ is a matroid, then a simple matroid $M^{\mathrm{\prime }}$ with the same rank as $M$ is an adjoint of $M$ if there is an inclusion-reversing embedding $\phi$ of the lattice of flats of $M$ into the lattice of flats of $M^{\mathrm{\prime }}$ such that $\phi$ maps the hyperplanes of $M$ bijectively onto the points of $M^{\mathrm{\prime }}$. In this note, we provide a proof that the class of matroids with an adjoint is minor-closed.