Fr. Karl Josef Becker, S.J.,cardinal designate says the Church of Christ is identified with the Catholic Church. The Church of Christ is the Catholic Church. (1)
The Jesuit priest who is to be made a cardinal this week is saying extra ecclesiam nulla salus. The true Church of Christ exists in only the Catholic Church he says and elements of this one true Church could exist in the Orthodox Christian churches and those in partial communion with the Catholic Church.(2)
The cardinal designate is affirming the dogma extra ecclesiam nulla salus which says all need to convert into the Catholic Church for salvation. The dogma Cantate Domino, Council of Florence specifically mentions the Orthodox Christians and Protestants.
According to the dogma extra ecclesiam nulla salus the Church of Christ is the Catholic Church.
Lumen Gentium 8 and 16 suggest that there is the possibility of a non Catholic being saved however since these cases are not defacto known to us Vatican Council II does not contradict the dogma.-Lionel Andrades
An Examination of Subsistit in: A Profound Theological Perspective
Fr. Karl Josef Becker, S.J. http://www.ewtn.com/library/Theology/subsistitin.htm
But the Council had chosen the word subsistit exactly in order to make clear that one sole 'subsistence' of the true Church exists, whereas outside her visible structure only elementa Ecclesiae exist; these —
being elements of the same Church — tend and conduct toward the Catholic Church (Lumen Gentium, n. 8)".