From the Catechism of the Catholic Church:

 “The Church of Christ is really present in all legitimately organized local groups of the faithful, which, in so far as they are united to their pastors, are also quite appropriately called Churches in the New Testament. . . . In them the faithful are gathered together through the preaching of the Gospel of Christ, and the mystery of the Lord’s Supper is celebrated. . . . In these communities, though they may often be small and poor, or existing in the diaspora, Christ is present, through whose power and influence the One, Holy, Catholic, and Apostolic Church is constituted.”312
833 The phrase “particular Church,” which is first of all the diocese (or eparchy), refers to a community of the Christian faithful in communion of faith and sacraments with their bishop ordained in apostolic succession.313 These particular Churches “are constituted after the model of the universal Church; it is in these and formed out of them that the one and unique Catholic Church exists.”314
834 Particular Churches are fully catholic through their communion with one of them, the Church of Rome “which presides in charity.”315 “For with this church, by reason of its pre-eminence, the whole Church, that is the faithful everywhere, must necessarily be in accord.”316 Indeed, “from the incarnate Word’s descent to us, all Christian churches everywhere have held and hold the great Church that is here [at Rome] to be their only basis and foundation since, according to the Savior’s promise, the gates of hell have never prevailed against her.”317

836 “All men are called to this catholic unity of the People of God. . . . And to it, in different ways, belong or are ordered: the Catholic faithful, others who believe in Christ, and finally all mankind, called by God’s grace to salvation.”320
837  “Fully incorporated into the society of the Church are those who, possessing the Spirit of Christ, accept all the means of salvation given to the Church together with her entire organization, and who – by the bonds constituted by the profession of faith, the sacraments, ecclesiastical government, and communion – are joined in the visible structure of the Church of Christ, who rules her through the Supreme Pontiff and the bishops. Even though incorporated into the Church, one who does not however persevere in charity is not saved. He remains indeed in the bosom of the Church, but ‘in body’ not ‘in heart.'”321
838 “The Church knows that she is joined in many ways to the baptized who are honored by the name of Christian, but do not profess the Catholic faith in its entirety or have not preserved unity or communion under the successor of Peter.”322 Those “who believe in Christ and have been properly baptized are put in a certain, although imperfect, communion with the Catholic Church.”323

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