Catechism of the Catholic Church
C. Para. 253: The Trinity is One. We do not confess three Gods, but one God in three persons, the “consubstantial Trinity” (Council of Constantinople II [553]: DS 421). The divine persons do not share the one divinity among themselves but each of them is God whole and entire: “The Father is that which the Son is, the Son that which the Father is, the Father and the Son that which the Holy Spirit is, i.e., by nature one God” (Council of Toledo XI [675]: DS 530:26). In the words of the Fourth Latern Council (1215): “Each of the persons is that supreme reality, viz., the divine substance, essence or nature” (Latern Council IV [1215]: DS 804).
Para. 254: The divine persons are not really distinct from one another. “God is one but not solitary” (Fides Damasi: DS 71). “Father,” “Son,” “Holy Spirit” are not simply names designating modalities of the divine being, for they are really distinct from one another: “He is not the Father who is the Son, nor is the Son he who is the Father, nor is the Holy Spirit he who is the Father or the Son” (Council of Toledo XI [675]: DS 530:25). They are distinct from one another in their relations of origin: “It is the Father who generates, the Son who is begotten, and the Holy Spirit who proceeds” (Latern Council IV (1215): DS 804). The divine Unity is Triune.