Actually, the Doctrine was defined much earlier than the 4th century. Tertullian discussed its aspects somewhere ca. 180. Additionally, the phrase does occur in Scripture... Matthew 28:19 quotes Yeshua ""Therefore go and make disciples of all nations, baptizing them in the name of the Father and of the Son and of the Holy Spirit." (Ch. 28 v. 19).
The dual nature of God is inferred in the very first phrase in the Old Covenant... "In the beginning, God..." (******* bara elohim). The Hebrew word translated as God is Elohim.... the plural of Eloha, but used in this verse as The God (singular) of Israel but in a plural tense.
The Apostle John is generally conceded to be the latest writer in the New Covenant... in his Gospel at Ch.1, vs. 1 he submits "In the beginning was the Word, and the Word was with God, and the Word was God." The clear implication is that Yeshua was the Word and had always existed as God, yet with God. Additionally, in Beresh!t (Genesis) The Spirit of God hovered over the surface of the waters... (Ch. 1, vs. 2)..
Several places the Doctrine is clearly enunciated, in my opinion...