“That means only the Orthodox are true Churches based on the definition of St. Ignatius of Antioch from 105 A.D.”
And what, pray tell, did “St. Ignatius” say?
The local Catholic diocese is the fullness of the Church unto itself under the rule of its bishop.
Vatican II’s document Lumen Gentium says:
Bishops, therefore, with their helpers, the priests and deacons, have taken up the service of the community, (11*) presiding in place of God over the flock,(12*) whose shepherds they are, as teachers for doctrine, priests for sacred worship, and ministers for governing.(13*) And just as the office granted individually to Peter, the first among the apostles, is permanent and is to be transmitted to his successors, so also the apostles’ office of nurturing the Church is permanent, and is to be exercised without interruption by the sacred order of bishops. (14*) Therefore, the Sacred Council teaches that bishops by divine institution have succeeded to the place of the apostles, (15*) as shepherds of the Church, and he who hears them, hears Christ, and he who rejects them, rejects Christ and Him who sent Christ.(149)(16*)
21. In the bishops, therefore, for whom priests are assistants, Our Lord Jesus Christ, the Supreme High Priest, is present in the midst of those who believe. For sitting at the right hand of God the Father, He is not absent from the gathering of His high priests,(17*) but above all through their excellent service He is preaching the word of God to all nations, and constantly administering the sacraments of faith to those who believe, by their paternal functioning.(150) He incorporates new members in His Body by a heavenly regeneration, and finally by their wisdom and prudence He directs and guides the People of the New Testament in their pilgrimage toward eternal happiness. These pastors, chosen to shepherd the Lord’s flock of the elect, are servants of Christ and stewards of the mysteries of God,(151) to whom has been assigned the bearing of witness to the Gospel of the grace of God,(152) and the ministration of the Spirit and of justice in glory.(153)
For the discharging of such great duties, the apostles were enriched by Christ with a special outpouring of the Holy Spirit coming upon them,(154) and they passed on this spiritual gift to their helpers by the imposition of hands,(155) and it has been transmitted down to us in Episcopal consecration.(18*) And the Sacred Council teaches that by Episcopal consecration the fullness of the sacrament of Orders is conferred, that fullness of power, namely, which both in the Church’s liturgical practice and in the language of the Fathers of the Church is called the high priesthood, the supreme power of the sacred ministry.(19*) But Episcopal consecration, together with the office of sanctifying, also confers the office of teaching and of governing, which, however, of its very nature, can be exercised only in hierarchical communion with the head and the members of the college. For from the tradition, which is expressed especially in liturgical rites and in the practice of both the Church of the East and of the West, it is clear that, by means of the imposition of hands and the words of consecration, the grace of the Holy Spirit is so conferred,(20*) and the sacred character so impressed,(21*) that bishops in an eminent and visible way sustain the roles of Christ Himself as Teacher, Shepherd and High Priest, and that they act in His person.(22*) Therefore it pertains to the bishops to admit newly elected members into the Episcopal body by means of the sacrament of Orders.
http://www.vatican.va/archive/hist_councils/ii_vatican_council/documents/vat-ii_const_19641121_lumen-gentium_en.html