Christ “established here on earth” only one Church … This Church, constituted and organised in this world as a society, subsists in the Catholic Church, governed by the successor of Peter and the Bishops in communion with him”.
… ‘subsistence’ means this perduring, historical continuity and the permanence of all the elements instituted by Christ in the Catholic Church, in which the Church of Christ is concretely found on this earth.
It is possible, according to Catholic doctrine, to affirm correctly that the Church of Christ is present and operative in the churches and ecclesial Communities not yet fully in communion with the Catholic Church, on account of the elements of sanctification and truth that are present in them.[9] Nevertheless, the word “subsists” can only be attributed to the Catholic Church alone precisely because it refers to the mark of unity that we profess in the symbols of the faith (I believe… in the “one” Church); and this “one” Church subsists in the Catholic Church.
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“It is through the celebration of the Eucharist of the Lord in each of these Churches that the Church of God is built up and grows in stature”.[16] However, since communion with the Catholic Church, the visible head of which is the Bishop of Rome and the Successor of Peter, is not some external complement to a particular Church but rather one of its internal constitutive principles, these venerable Christian communities lack something in their condition as particular churches.[17]
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According to Catholic doctrine, these Communities do not enjoy apostolic succession in the sacrament of Orders, and are, therefore, deprived of a constitutive element of the Church. These ecclesial Communities which, specifically because of the absence of the sacramental priesthood, have not preserved the genuine and integral substance of the Eucharistic Mystery[19]cannot, according to Catholic doctrine, be called “Churches” in the proper sense. [20]