How did Paul prove that Christians are children of God?

How Paul proved that Christians are children of God (Galatians 3:26 - 4:7; Romans 8:14-17)

• Paul taught that in Christ Jesus we are all children of God through faith. It is faith in Christ, not the works of the law, that makes a person a child of God.
• He pointed to baptism: as many as have been baptised into Christ have put on Christ. In Him there is neither Jew nor Greek, slave nor free, male nor female, for all are one in Christ Jesus.
• He argued that those who belong to Christ are Abraham's offspring and heirs according to the promise.
• Paul used the illustration of an heir who is still a child: while under age he is no better than a slave, kept under guardians until the time set by the father. So too, before Christ came, people were enslaved under the law and the elemental principles of the world.
• But when the fullness of time had come, God sent forth His Son, born of a woman, born under the law, to redeem those under the law, so that we might receive adoption as sons.
• As proof of this sonship, God has sent the Spirit of His Son into our hearts, crying, Abba, Father. The very cry of the Spirit within believers testifies that they are God's children.
• Paul concluded, So you are no longer a slave but a son, and if a son, then an heir through God. In Romans he adds that all who are led by the Spirit of God are sons of God, and that the Spirit bears witness with our spirit that we are children of God, and if children, then heirs, heirs of God and fellow heirs with Christ.

Thus Paul proved Christian sonship by faith in Christ, by baptism into Christ, by the redemption and adoption accomplished through God's Son, and by the inward witness of the Holy Spirit who cries, Abba, Father.