Instead, Jesus is a priest "on the order of Melchizedek." Melchizedek was a mysterious priest named in Genesis, who exerts some influence over Abraham. This reading takes time to prove the parallel between Jesus and Melchizedek and then suggest several implications. However, the important thing to understand is that Jesus is not a Levitical priest; by offering himself as a perfect sacrifice, Jesus initiates a new covenant between God and humankind that fulfills the promise of the covenant with Abraham.
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The second reading describes this new covenant, which replaces the older covenant. It is a better covenant, offering complete salvation. Further, it recognizes that the descendants of Abraham had eventually turned away and rejected the covenant between God and Abraham. Still, through Jesus, God finds a way to fulfill the promises of the prophets and offer salvation and hope.
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Reading the Bible in Its Entirety
If you are planning to read the Bible in its entirety, you should read Hebrews 7-8 today.