Canto 2 -
Ayodhyā-kāṇḍa
Chapter 110: Vasiṣṭha Requests Rāma to Accept the Throne
Text 2.110.16

तांस्तु सर्वान्प्रतिव्यूह्य युद्धे राजा प्रवासितः।
स च शैलवरे रम्ये बभूवाभिरतो मुनिः॥

tāṁs tu sarvān prativyūhya yuddhe rājā pravāsitaḥ
sa ca śaila-vare ramye babhūvābhirato muniḥ

tān tu sarvān = all of them; prativyūhya = having faced; yuddhe = in battle; rājā = King Asita; pravāsitaḥ = was forced ti leave [his kingdom]; saḥ = he; ca = and; śaila-vare = the best of mountains; ramye = in the pleasant Himalayas; babhūva = became; abhirataḥ = a practicing; muniḥ = sage.

“Having faced all of them in battle, King Asita was forced to leave [his kingdom] and he became a practicing sage in the pleasant Himalayas, the best of mountains.

It is implied here that had he not become a sage, he would have been banished from the mountain too.