1. Meaning of the term inerrant: The sixty-six books of the Protestant canon are divinely-inspired, and therefore inerrant (since God cannot lie) in the original writings (autographs). This process of inspiration is confluent: God used the writers to communicate exactly what God wanted, yet did so without overriding their personalities. For a detailed analysis, see Carl Henry, God, Revelation and Authority, vols. 2-4 especially.
2. There are cogent arguments from nature and humanity that an personal-infinite God exists.
3. If (2), then this God could inspire writings to say what he wants them to say. See Part II of Groothuis, Christian Apologetics and Francis Schaeffer, “Is Propositional Revelation Nonsense?” in He is There and He is Not Silent.
4. The text of the New Testament has been reliably transmitted to us today (textual criticism). See chapter 19 of Christian Apologetics.
5. The New Testament passes the tests of reliable history. See chapter 19 of Christian Apologetics.
6. The New Testament presents Jesus as God-incarnate, given Jesus’ claims, credentials, and achievements.
7. Jesus endorsed the divine authority of the Old Testament, directly and indirectly. See chapter 20 of Christian Apologetics.
8. Therefore, the Old Testament is divinely inspired/inerrant. See chapter 20 of Christian Apologetics.
9. Jesus authorized the Apostles to preserve his teachings. See chapter 20 of Christian Apologetics.
10. Therefore the New Testament, which is apostolically authorized directly or indirectly, is divinely-inspired/inerrant. See chapter 20 of Christian Apologetics.
11. Therefore, the sixty-six books of the Bible are divinely-inspired/inerrant. See chapter 20 of Christian Apologetics.
12. Bonus: While textual transmission has not been inerrant, it has been very reliable. Thus, we can say that the best translations today are infallible; that is, they will not mislead us on anything to which they speak.
13. Every Christian should have some understanding of the epistemological basis of their worldview! No “leap of faith” is needed.