5 For Moses writes that the law’s way of making a person right with God requires obedience to all of its commands. 6 But faith’s way of getting right with God says, “Don’t say in your heart, ‘Who will go up to heaven?’ (to bring Christ down to earth). 7 And don’t say, ‘Who will go down to the place of the dead?’ (to bring Christ back to life again).” 8 In fact, it says,
“The message is very close at hand; it is on your lips and in your heart.”
And that message is the very message about faith that we preach:
9 [P] If you openly declare that Jesus is Lord and [Q] believe in your heart that God raised him from the dead, [R then] you will be saved.
10 For it is by believing in your heart that you are made right with God, and it is by openly declaring your faith that you are saved. 11 As the Scriptures tell us, “Anyone who trusts in him will never be disgraced.” 12 Jew and Gentile are the same in this respect. They have the same Lord, who gives generously to all who call on him. 13 For “Everyone who calls on the name of the Lord will be saved.”
14 But how can they call on him to save them unless they believe in him? And how can they believe in him if they have never heard about him? And how can they hear about him unless someone tells them? 15 And how will anyone go and tell them without being sent? That is why the Scriptures say, “How beautiful are the feet of messengers who bring good news!”
16 But not everyone welcomes the Good News, for Isaiah the prophet said, “Lord, who has believed our message?”  [NLT]
17 Consequently, faith comes by hearing, and hearing through the word about Christ. [ LEB ]
The Law given by Moses, which came 400 years after the promise of blessing through faith, did not invalidate the promise. Rather, the law which demanded perfect obedience to every law in absolute precision, to which no mortal was able to do, illustrated how great the need was for God’s blessing to be established by free grace and faith.
Consider just one small issue. Man is sinful. God is morally and intellectually infinitely a cut above all things and is dreadfully awesome. God demands respect and obedience. How then, even if a sinful man somehow realizes how sinful he is and wants to approach God for help, on what ground can he even approach God in the first place? Regarding the King of Glory to whom the doors of heaven opened for in Psalm 24, it is asked, “who is able to ascend the hill of Yahweh, and who has clean hands?” The answer is that sinful man is not. Man is not even able to ask God for help, because man cannot even approach God to begin with to even ask.
Therefore, Paul quotes Moses in Deut. 9:4. The word of faith tells us that Jesus is our high priest who redeems us. He does the hard work to reconcile God and man together, so that, upon being reconciled man might fully enjoy the lavish blessings of their heavenly Father. To be reconciled man needs to go to God. They need a death (i.e. a sacrifice to appease God). And they need to escape their own deaths and curse. Jesus did all this. He came down from heaven to this dusty earth. He was the cursed, wrath-appeasing atonement for God’s chosen ones. Then by the power of the Father, Jesus in endless power of life destroyed death and sits at the right hand of the Majesty.
Hebrews 10:18 has a very simple way to sum this up, [NLT] “And when sins have been forgiven, there is no need to offer any more sacrifices.” Jesus WAS a sacrifice for sin already, and thus, sin WAS forgiven at that definite time and place of His atoning work. The preacher of Hebrews is so bold as to say that Jesus is “sanctifying us whom He has ALREADY perfected.” If sin was not forgiven [past tense] then there still needs a sacrifice for it, this is the implication of Hebrews 10.
Consider the moment you sin, or you yet again fell to your besetting sin. Do you try to mentally beat yourself up, hoping this will make you feel better? Or do you mentally berate yourself so that this will gain a small amount of God’s approval, so that it will make it easier on your mind to approach God to ask forgiveness? If so, then you just used a “sacrifice,” albeit a small one, to find forgiveness. You just pulled Jesus down from heaven! You just yanked Him up from the grave! How dare you! Do you fear God at all?
Where there is forgiveness, there is no longer any sacrifice. None.
Paul therefore gives this quick argument to show what we ought to do in light of God’s redemption. It is about faith in God’s revelation.
The nature of the argument is best suited for Natural deduction, due to the conjunction in it. (P • Q) ⸧ R / P • Q ⸫ R
The argument is set up for a placeholder, to which you place yourself into. That is, have you assented to the truth of God’s redemption and confessed it? If so, you place yourself directly into the argument. And so, it could be used for a First Order Predicate logic (see my argument for Romans 8:28-30) For simplicity we will use a basic propositional argument with one conjunction in it.
D.1. (P) If you assented that the Father raised Jesus from the dead, and (Q) confess that Jesus is Lord, (R) then it is necessary you are saved.
D.2. (P) It is true that I have assented that the Father raised Jesus from the dead, and (Q) confess that Jesus is Lord.
D.3. Thus, I have been saved.
A few quick things. Faith means a mental assent. Many lie to themselves they assent that proposition “X” is truth, when in fact they might merely wish it were true or something else. They are like the man in James, who after seeing themselves in the mirror, walk away and forget. They did not really assent to God’s truths to begin with. To believe these gospel premises are true without deceiving yourself, you must be born again.
Next, in context Paul quotes two O.T. passages where one says, “believe,” and the other “confess,” which is why his argument has both. However, when one is born again by the Spirit, then one means the other. If the Spirit causes you to see and believe in the Kingdom of God, then you will necessarily confess it—like a new born baby breaths because it is alive. And so, an argument or statement can merely state one and the other is implied to be there, which Paul does.
Everyone who calls on the name of the Lord will be saved.
This enthymeme is more partial than the first. It is a categorical truth, that is implied for us to apply ourselves to it. All [persons who call on the Lord] are [those who will be saved].
E.1. All [persons who call on the Lord] are [those who will be saved].
E.2. All [Oshea] is [he who calls on the Lord].
E.3. Therefore, [Oshea] is [he who will be saved].
The conclusion remark in verse 17, “consequently,” can be a summary statement for a doctrine, “All [faith] is [that which comes by hearing the Word of God]. Or it could be an enthymeme chain argument for necessary connections regarding what we ought to do.
Paul is making a logical order. If P then Q, …if Q then R.
“(P) If faith comes by hearing the declared Word, (Q) then someone must be declaring the Word.” The moral implication is we need to declare the Word. Thus, “(Q) if someone must be declaring the Word, (R) then we—the church—ought to be doing this.”
  added by author, and verse separations.
 3 Who may climb the mountain of the LORD?
Who may stand in his holy place?
4 Only those whose hands and hearts are pure,
who do not worship idols
and never tell lies.
5 They will receive the LORD’s blessing
and have a right relationship with God their savior.
6 Such people may seek you
and worship in your presence, O God of Jacob.
7 Open up, ancient gates!
Open up, ancient doors,
and let the King of glory enter. (Psalm 24 NLT)
 Hearing the word of God can come in many ways. God gave His word directly in dreams before, without any person (or sensation of sight, hearing, smelling, toughing) involved. Having His chosen one preach it (whether by speaking or writing) is the normal occasion God directly puts knowledge of Himself in the mind, but this is not the only way. The point is for there to be the possibility for faith to happen, then there must be knowledge of God first.