The difference between believers who rested in Christ only, and those who trusted in the law, is explained by the histories of Isaac and Ishmael. These things are an allegory, wherein, beside the literal and historical sense of the words, the Spirit of God points out something further.
Hagar and Sarah were apt emblems of the two different dispensations of the covenant. The heavenly Jerusalem, the true church from above, represented by Sarah, is in a state of freedom, and is the mother of all believers, who are born of the Holy Spirit.
They were by regeneration and true faith, made a part of the true seed of Abraham, according to the promise made to him.