Since verse 13 spoke about "God swearing an Oath to Abraham" we see the Hebrew writer explaing what that means also.
The constant examples of the OT should be clear.
The warnings giving in the OT to the Jews wasn't heeded but them neither.
It's being used here in the entire book of Hebrews as example to make a serious point about continuing in the Faith.
Chapter 6 ends with Melchisedec and Christ entering the Holy of Holies. so the next Chapter continues the thought on Melchisedec and that Jesus is greater then the order of the Priesthood.
The LIT is also below it for reference.
Verses 16
16. For men verily swear by the greater: and an oath for confirmation is to them an end of all strife.
17. Wherein God, willing more abundantly to shew unto the heirs of promise the immutability of his counsel, confirmed it by an oath:
18. That by two immutable things, in which it was impossible for God to lie, we might have a strong consolation, who have fled for refuge to lay hold upon the hope set before us:
19. Which hope we have as an anchor of the soul, both sure and stedfast, and which entereth into that within the veil;
20. Whither the forerunner is for us entered, even Jesus, made an high priest for ever after the order of Melchisedec.
men indeed For by the greater swear, and of all {is} to them contradiction an end for confirmation the oath.
In which more abundantly resolving - God to show to the heirs of the promise the unchangeableness of the counsel of Him,
He interposed by an oath that through two things unchangeable,
in which {it was} impossible to lie God,
a strong consolation we could have,
those having fled to lay hold of the set in front of {us} hope,
which as an anchor we have of the soul,
secure both and firm,
and
entering into the inner {side} of the curtain,
where a forerunner for us entered--
Jesus--
according to the order of Melchizedek, High Priest becoming for the age.