Albert Barnes Commentary Galatians 3:7

"Know therefore that they that are of faith, the same are sons of Abraham." — Galatians 3:7 (ASV)

Know you therefore, etc. Learn from this case. It is an inference that follows, that all those who believe are the children of Abraham.

They which are of faith. These are those who believe and are justified in this way.

Are the children of Abraham. Abraham was the "father of the faithful." The most remarkable trait in his character was his unwavering confidence in God. Those who demonstrated the same trait, therefore, were worthy to be called his children. They would be justified in the same way, and in the same manner meet the approval of God.

It is implied here that it was sufficient for salvation to have a character that would make it proper to say that we are the children of Abraham. If we are like him, if we demonstrate the same spirit and character, we may be sure of salvation.