‘Semi-modalism’ is the false doctrine that teaches that the three real persons of the Trinity are together a single person. Most semi-modalists, however, refuse to use the term “person” for the Trinity, although conceptually they treat the Trinity as a whole as a person in every way except using that term for it.
The London Baptist Confession of 1689 says in its second chapter:
“The Lord our God is but one only living and true God; whose subsistence is in and of himself, infinite in being and perfection…
In this divine and infinite Being there are three subsistences, the Father, the Word or Son, and Holy Spirit, of one substance, power, and eternity, each having the whole divine essence, yet the essence undivided: the Father is of none, neither begotten nor proceeding; the Son is eternally begotten of the Father; the Holy Spirit proceeding from the Father and the Son; all infinite, without beginning, therefore but one God, who is not to be divided in nature and being, but distinguished by several peculiar relative properties and personal relations; which doctrine of the Trinity is the foundation of all our communion with God, and comfortable dependence on him.”
Here we see them begin their treatment of the Trinity by saying that the one God is a person “whose subsistence is in and of himself”. Subsistence is a philosophical term for person, when it refers to something of a rational nature, such as God, or an angel, or a man. What is more clear in identifying him as a single person is their explicit use of singular personal pronouns.