16:13 into all truth. Christ had yet “many things to say” (John 16:12) to His disciples, but these would be revealed through the coming Spirit of truth. Not only would the Holy Spirit enable them to remember all Christ had said (John 14:26), but would eventually through divine inspiration by the Spirit reveal “all truth” needed for the future ministry of Christians in the world. These promises amount to Christ’s promise of the continuation and completion of God’s written Word. He had already on various occasions authenticated the Old Testament (e.g., Matthew 5:18; Luke 24:44; John 10:35); now He also authenticated the yet-to-be-written New Testament.
16:13 speak of himself. Christ is not saying here that the Holy Spirit will never speak about Himself (there is much in the New Testament about the Holy Spirit, all of which was inspired by Him), but rather, He will not speak independently of the Father and the Son. Thus, the words of the New Testament are authenticated by the triune God.
16:13 things to come. A prominent component of these future revelations would be—just as in the Old Testament—revelations about the future. In fact, every New Testament writer has included prophetic passages in his writings, most of all John himself, in the book of Revelation.