Translation
If anyone is of the opinion that he is a prophet, or is spiritual, let him fully recognize that the things I am writing to you are the commands of THE LORD.
Paraphrase
If anyone thinks he has something worth sharing in the meeting of God’s people because God has given him something special to share, or if he thinks he is spiritually sound, he should acknowledge that what I am writing to you is not something I made up for it fits the rest of the commands given to us by THE SUPREME RULER.
PAUL KNEW HE HAD THE BACKING OF SCRIPTURE AND HIS OPPONENTS DID NOT
Whether one is focusing on orderliness in worship, the proper ways to speak in tongues, or the issue of the authority of men and women, there has always been opposition to these things and that opposition comes from the flesh. In the various passages about the role of women, Paul says things that indicate he is aware of resistance to what he is saying, that is why he makes it a priority to point out that this is not just his opinion, it has deep roots. In his treatment of the issue of authority for men and women he sometimes points to creation, or to the fall of Adam and Eve into sin, or to the Law in general. To this I will add the fact that Jesus did not change these aspects of the Law when He established His New Covenant. All this goes together to build a strong foundation for the idea that there are clear lines of authority which God has established.
We should not be like the Corinthians and follow someone just because he claims to have spiritual authority or an impressive spiritual gift. If someone opposes or violates key Biblical principles, he should be given no authority in the local congregation. Anyone who disturbs the lines of authority God has established or ignores them, will suffer negative consequences.