I. They, whom God has accepted in His Beloved, effectually called, and sanctified by His Spirit, can neither totally nor finally fall away from the state of grace, but shall certainly persevere therein to the end, and be eternally saved.[1]
II. This perseverance of the saints depends not upon their own free will, but upon the immutability of the decree of election, flowing from the free and unchangeable love of God the Father;[2] upon the efficacy of the merit and intercession of Jesus Christ,[3] the abiding of the Spirit, and of the seed of God within them,[4] and the nature of the covenant of grace:[5] from all which arises also the certainty and infallibility thereof.[6]
III. Nevertheless, they may, through the temptations of Satan and of the world, the prevalency of corruption remaining in them, and the neglect of the means of their preservation, fall into grievous sins;[7] and, for a time, continue therein:[8] whereby they incur God's displeasure,[9] and grieve His Holy Spirit,[10] come to be deprived of some measure of their graces and comforts,[11] have their hearts hardened,[12] and their consciences wounded;[13] hurt and scandalize others,[14] and bring temporal judgments upon themselves.[15]
Westminster Confession of Faith (scripture references at site)
Actually, the Apostle Paul claimed those to whom he wrote were Christians in the introduction to both epistles.
Of course he does. He is writing to the church at Corinth. If your priest were to go into the church wouldn't he address everyone as a Catholic? You don't start singling out people. But if you know that the church is holding all sort of drunken orgies and people are not living a Christ-like life, I would hope the priest would have a few choice words to say to them. It is not the responsibility of the priest to tell people they're not a believer. But it is his responsibility to tell them they're acting like pagans (and some of them might be). One can certainly tell them they REALLY, REALLY need to examine themselves if they are in the faith but we can't tell them they're not saved (although we might have our doubts).
Paul, an apostle of Jesus Christ by the will of God
Do you notice anything here about the will of God???