ESV Reformation Study Bible – Heb 7:3
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Heb 7:3

7:3 Some believe that Melchizedek is a preincarnate appearance of Christ, but this is unlikely since terms of comparison and analogy are used: (a) he “resembles the Son of God” (a comparison of the Son with Himself would be odd); (b) the Son became High Priest “after the order of Melchizedek” (6:20) later, through His incarnation, atoning death, and exaltation. In addition, in Gen. 14 Melchizedek is presented as one who has a recognized political position (king of Salem), whereas Old Testament theophanies are brief and exceptional.

without father . . . mother . . . beginning of days nor end of life. While most figures in Genesis are located in a genealogical line, Melchizedek appears without ancestors or progeny, and without notice of his birth or death. The Holy Spirit has described him in a way that is prophetic of Christ.

genealogy. The appointment of priests in the line of Melchizedek is without regard to ancestry, since no genealogy is recorded for this line.