In classical logic, the law of non-contradiction (LNC) (or the law of contradiction (PM) or the principle of non-contradiction (PNC), or the principle of contradiction) is the second of the three classic laws of thought. It states that contradictory statements cannot both be true in the same sense at the same time, e.g. the two propositions "A is B" and "A is not B" are mutually exclusive.which can be found here:
The Second Vatican Council in Lumen Gentium, the Dogmatic Constitution on the Church stated the following:
"This Sacred Council accepts with great devotion this venerable faith of our ancestors regarding this vital fellowship with our brethren who are in heavenly glory or who having died are still being purified; and it proposes again the decrees of the Second Council of Nicea, the Council of Florence and the Council of Trent. And at the same time, in conformity with our own pastoral interests, we urge all concerned, if any abuses, excesses or defects have crept in here or there, to do what is in their power to remove or correct them, and to restore all things to a fuller praise of Christ and of God. Let them therefore teach the faithful that the authentic cult of the saints consists not so much in the multiplying of external acts, but rather in the greater intensity of our love, whereby, for our own greater good and that of the whole Church, we seek from the saints 'example in their way of life, fellowship in their communion, and aid by their intercession.' On the other hand, let them teach the faithful that our communion with those in heaven, provided that it is understood in the fuller light of faith according to its genuine nature, in no way weakens, but conversely, more thoroughly enriches the latreutic worship we give to God the Father, through Christ, in the Spirit." (Lumen Gentium, 51)which means that Vatican II reaffirmed the following:
"The most Holy Roman Church firmly believes, professes and preaches that none of those existing outside the Catholic Church, not only pagans, but also Jews and heretics and schismatics, can have a share in life eternal; but that they will go into the eternal fire which was prepared for the devil and his angels, unless before death they are joined with Her; and that so important is the unity of this ecclesiastical body that only those remaining within this unity can profit by the sacraments of the Church unto salvation, and they alone can receive an eternal recompense for their fasts, their almsgivings, their other works of Christian piety and the duties of a Christian soldier. No one, let his almsgiving be as great as it may, no one, even if he pour out his blood for the Name of Christ, can be saved, unless he remain within the bosom and the unity of the Catholic Church." (Pope Eugene IV, the Bull Cantate Domino, 1441.)What does Vatican II's reaffirmation truly mean? It can mean only one and only one thing:
Visible or not, de facto or de jure, vincibly or invincibly ignorant, explicit or implicit, in voto or ex voto, baptism in re or in voto, every human being, without exception, must end his/her life in the "bosom and unity of the Catholic Church." This proclamation from the Council of Florence, an ecumenical Council of the Catholic Church, is ex cathedra, without error, infallible, and irreformable for all time and eternity.That's what Vatican II reaffirmed in Lumen Gentium 51, if only "implicitly."