The
next Princess Teishi, the mansions that she
inherited were Biwa-dono Palace
on Konoe Oji (aka Yomeimon Oji) which runs
through Daidairi's Yomei-mon Gate, and Oi-dono
on Oi-no-mikado Oji which runs
through Daidairi's Ikuho-mon Gate,
so her
title had
a "mon" because of that.