Is it true that by the end of the fourth century christianity was the official religion of the roman empire based on the following text?

Nicene Christianity became the state church of the Roman Empire with the Edict of Thessalonica in 380 AD, when Emperor Theodosius I made it the Empire's sole authorized religion. The Eastern Orthodox Church, Oriental Orthodoxy, and the Catholic Church each claim to be the historical continuation of this church in its original form, but do not identify with it in the caesaropapist form that it took later. Unlike Constantine I, who with the Edict of Milan of 313 AD had established tolerance for Christianity without placing it above other religions and whose involvement in matters of the Christian faith extended to convoking councils of bishops who were to determine doctrine and to presiding at their meetings, but not to determining doctrine himself, Theodosius established a single Christian doctrine (specified as that professed by Pope Damasus I of Rome and Pope Peter II of Alexandria) as the Empire's official religion.
yes