Yoshimitsu also was from the Minamoto clan who's founder was Emperor Seiwa (or Emperor Yozei), however he was almost ten generations removed from the former Emperor who was in the same Imperial lineage, so he was not considered to have the right to succeed to the throne.
義満も清和天皇（又は陽成天皇）に始まる源氏ではあるが、代数が当時の天皇から十数代も離れていたため皇族としての資格はないものと見做されていた。