Tertullian was giving the part that matches John 10:30 and the concept of unity.
Not very complicated.
Why would he only give "part" of 1 John 5:7 when the whole Comma would not be out of place at all!
It would aid his argument.
Tertullian of Carthage (circa. A.D./C.E.)
Adversus Praxeam
Chapter 25.1
“Ita connexus Patris in Filio et Filii in Paracleto tres efficit cohaerentes alterum ex altero. ["Quoniam tres sunt, qui testimonium dant in cælo : Pater, Verbum, et Spiritus Sanctus : et hi] tres unum sunt." Non unus, quomodo dictum est, 'Ego et Pater unum sumus,' ad substantiae unitatem non ad numeri singularitatem.”
"Thus the connection of the Father in the Son, and of the Son in the Paraclete, thereby proving that these three [masculine identities [Or: "these three persons"]] are connected together, with each one originating from out of the other. [“For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost: and] these three are one”, not one [masculine identity [Or: " not a singular masculine identity" "not one person"]], even as it says "I and the Father, we are one," by the uniting of the substances, not by the singularity of the numbers."
It would list the "persons" "individually" - combating beautifully Praxeas undifferentiated One-ness.
Tertullian of Carthage (circa.145-225 C.E.)
Adversus Praxeam
Chapter 26.9
"et novissime mandans ut tinguerent in patrem et filium et spiritum sanctum, non in unum :
nam nec semel, sed ter, ad singula nomina, in personas singulas tinguimur."
“And lastly, commanding that we should be immersed in the Father and the Son and the Holy Spirit, not into (unum) the one,
since it is not once, but three times, that we should be immersed for each individual name, in each person individually."