Not getting into a detailed debate on this subject as it bores me. You can preach EENS very well without ever mentioning bod. But if you deny or attack bod, the Church will push back, as it did to SBC. The three AAS docuмents I cited are very clear. Whoever wants to learn the teaching of the Church can learn it from those. Preach EENS, invite souls to baptism or confession, and to the Holy Eucharist for perseverance in grace, and you will do well. Keep attacking or denying doctrine or dogma, and you will get confused, claim dozens of Popes or even hundreds of years of Popes are heretics (like Orthodox do), possibly lose the faith and become a heretic or a schismatic yourself, lapse into Photian Orthodoxy as ihsv mentioned, or even apostatize completely and become a worldling again. Not good. The Holy Office letter btw clearly teaches EENS in the Catholic sense.
"Accordingly, the Most Eminent and Most Reverend Cardinals of this Supreme Congregation, in a plenary session held on Wednesday, July 27, 1949, decreed, and the august Pontiff in an audience on the following Thursday, July 28, 1949, deigned to give his approval, that the following explanations pertinent to the doctrine, and also that invitations and exhortations relevant to discipline be given:
We are bound by divine and Catholic faith to believe all those things which are contained in the word of God, whether it be Scripture or Tradition, and are proposed by the Church to be believed as divinely revealed, not only through solemn judgment but also through the ordinary and universal teaching office (<Denzinger>, n. 1792).
Now, among those things which the Church has always preached and will never cease to preach is contained also that infallible statement by which we are taught that there is no salvation outside the Church.
However, this dogma must be understood in that sense in which the Church herself understands it. For, it was not to private judgments that Our Savior gave for explanation those things that are contained in the deposit of faith, but to the teaching authority [i.e. Magisterium - MM] of the Church.
Now, in the first place, the Church teaches that in this matter there is question of a most strict command of Jesus Christ. For He explicitly enjoined on His apostles to teach all nations to observe all things whatsoever He Himself had commanded (Matt. 28: 19-20).
Now, among the commandments of Christ, that one holds not the least place by which we are commanded to be incorporated by baptism into the Mystical Body of Christ, which is the Church, and to remain united to Christ and to His Vicar, through whom He Himself in a visible manner governs the Church on earth.
Therefore, no one will be saved who, knowing the Church to have been divinely established by Christ, nevertheless refuses to submit to the Church or withholds obedience from the Roman Pontiff, the Vicar of Christ on earth."