Paul's letters often followed a pattern which included the following: salutation, thanksgiving, main body, and a farewell. In all of Paul's letters, with the exception of Galatians, the main theme of the letter is stated in the greeting and thanksgiving portion. In Paul's letter to the church at Corinth, the apostle addresses some issues in the Corinthian church, but in the greeting and thanksgiving section of this letter, Paul states his main purpose for the letter, which is that all believers belong to Christ Jesus:
"To God's church church at Corinth, to those who are sanctified in Christ Jesus and called as saints, with all those in every place who call on the name of Jesus Christ our Lord—both their Lord and ours." (1st Corinthians 1:2).
All who have called on the name of Jesus and accept him as Lord are "set-apart" and belong to Jesus, accepting his authority. Jesus is head of the church, and ultimately, Lord of all.
Paul often uses the servant/master relationship to describe what it means to belong to Christ. This would have been a familiar paradigm to those in the first century. Paul explains the role of God's servants in chapter 3, verse 5:
"What then is Apollos? And what is Paul? They are servants through whom you believed, and each has the role the Lord has given. I planted, Apollos watered, but God gave the growth. So then neither the one who plants nor the one who waters is anything, but only God who gives the growth." (1st Corinthians 3:5-8).
Paul addresses the issues of immoral church members, lawsuits, discipline within the church, glorifying God in mind, body, and spirit, principles of marriage, and unmarried people and widows. He warns the church about idolatry, the folly of human wisdom, and mistakes of Israel's past, so they do not repeat them. He teaches about spiritual gifts and how each person is given different gifts, but that they are to work together as the body of Christ in the exercise of those gifts. He addresses the issue of order in church meetings, as well. But the thread that runs through all these teachings is the theme of the centrality of Christ. In chapter 15, Paul says,
"Now, brothers, I want to clarify for you the gospel I proclaimed to you; you received it and have taken your stand on it. You are also saved by it, if you hold to the message I proclaimed to you--unless you believed for no purpose. For I passed onto you as most important what I also received: that Christ died for our sins according to the Scriptures, that He was buried, and that He was raised on the third day according to the Scriptures."
This is the reason believers belong to Christ. He paid the penalty for sin that separated us from a Holy God and made us enemies of God. Through Christ's sacrifice, believers are reconciled to God.
In chapter 12, verse 27 Paul explains that if anyone is in Christ, "Now you are the body of Christ, and individual members in it."