Your statement is supported here as well:
22. Eradication of the Akusala Cittas by the four
classes of Aryan disciples.
A Sotàpanna (Stream-Winner) eradicates the 1st,
2nd, 5th, 6th, and 11th types of consciousness as he has
destroyed the two Fetters (Saüyojana)—Sakkàyadiññhi
(Self-illusion) and Vicikicchà (Doubts).
A Sakadàgàmi (Once-Returner), who has attained
the second stage of Sainthood, weakens the potentiality of
the 9th and 10th types of consciousness, because he has
only attenuated the two Fetters—Kàmaràga (Sense-desire)
and Pañigha (Hatred).
An Anàgàmi (Never-Returner), who has attained the
third stage of Sainthood, eradicates the above two types of consciousness
as he has completely destroyed the said two Fetters.http://www.buddhanet.net/pdf_file/abhidhamma.pdf