I'm not willing to separate Paul's Message in Galatians 3 into pieces, if that's what you mean. Paul's Message there must be taken as a WHOLE, not torn into fragments with men's leaven added to it...
Gal 3:1-29
1 O foolish Galatians, who hath bewitched you, that ye should not obey the truth, before whose eyes Jesus Christ hath been evidently set forth, crucified among you?
2 This only would I learn of you, Received ye the Spirit by the works of the law, or by the hearing of faith?
3 Are ye so foolish? having begun in the Spirit, are ye now made perfect by the flesh?
4 Have ye suffered so many things in vain? if it be yet in vain.
5 He therefore That ministereth to you the Spirit, and worketh miracles among you, doeth He it by the works of the law, or by the hearing of faith?
Paul begins his Message with an idea that ought to be right up your alley, contrasting Faith against seeking to be saved by following the law. Some "false brethren" (Gal.2:4) were among those Gentile Galatians trying to get them to believe in Christ's Salvation by following the law.
6 Even as Abraham believed God, and it was accounted to him for righteousness.
7 Know ye therefore that they which are of faith, the same are the children of Abraham.
8 And the scripture, foreseeing that God would justify the heathen through faith, preached before the gospel unto Abraham, saying, In thee shall all nations be blessed.
9 So then they which be of faith are blessed with faithful Abraham.
All those 6-9 verses go together specifically speaking about Abraham in relation to Faith. Who's Faith? His AND ours. When God told Abraham in Gen.14-17 that through him ALL nations would be blessed, Paul is speaking of The Gospel Faith. That was one of the ways HOW The Gospel was also preached to Abraham. The Promise God gave Abraham then involved that very Faith eventually coming to the Gentiles also, i.e. to ALL nations being blessed through Abraham. That's what Paul's Message is here so far.
10 For as many as are of the works of the law are under the curse: for it is written, 'Cursed is every one that continueth not in all things which are written in the book of the law to do them.'
11 But that no man is justified by the law in the sight of God, it is evident: for, 'The just shall live by faith.'
12 And the law is not of faith: but, The man that doeth them shall live in them.
Then Paul contrasts the idea of the law between the idea of Faith a bit more, showing how they are two separate things. We are not justified by following the law, but by Faith on Jesus Christ. But the man that is a doer of the law shall live in them. All it means is that we can still do the things in the law that is good, for like Paul said in Rom.7, the law is good and just. But we are to NEVER think that the law can offer Salvation. Only by Faith on The Father through Christ Jesus crucified is Salvation accounted.
13 Christ hath redeemed us from the curse of the law, being made a curse for us: for it is written, 'Cursed is every one that hangeth on a tree:'
14 That the blessing of Abraham might come on the Gentiles through Jesus Christ; that we might receive the promise of the Spirit through faith.
Now Paul gives a bit more about Abraham's Faith in relation to The Gospel of Jesus Christ. Christ redeemed those who believe from the curse of the law, so that "the blessing of Abraham might come on the Gentiles through Jesus Christ". That whose 'blessing' might come on the Gentiles? The blessing God gave to Abraham!! Per Genesis 14-17 that blessing is about the Promise by Faith which God first gave to Abraham, and the things associated with that Promise of Salvation.
15 Brethren, I speak after the manner of men; Though it be but a man's covenant, yet if it be confirmed, no man disannulleth, or addeth thereto.
16 Now to Abraham and his seed were the promises made. He saith not, And to seeds, as of many; but as of one, And to thy seed, which is Christ.
God specifically made the Promise that it would come through Abraham and his seed. Christ's lineage goes all the way back to the man Adam through Abraham per Luke 3. When we read about God's Promise to Abraham later with Isaac, then with Jacob, then to Israel, etc., it is about that same Promise of The Gospel by Faith first given to Abraham.
17 And this I say, that the covenant, that was confirmed before of God in Christ, the law, which was four hundred and thirty years after, cannot disannul, that it should make the promise of none effect.
The Old Covenant didn't come until 430 years AFTER God had already given Abraham the Promise by Faith. God's Promise to Abraham by Faith was always FIRST, long before the law was given through Moses later. So the law cannot ever disannul that Promise by Faith which came first, nor ever make the Promise of none effect. It's simple.
18 For if the inheritance be of the law, it is no more of promise: but God gave it to Abraham by promise.
If the Promise by Faith God first given to Abraham was of inheritance by the law, then it would no longer be by promise.
19 Wherefore then serveth the law? It was added because of transgressions, till the seed should come to whom the promise was made; and it was ordained by angels in the hand of a mediator.
The law through Moses was added later BECAUSE OF TRANSGRESSIONS, up to the time when the seed would come unto whom Jesus Christ would manifest. It's simply about the time when Christ would die on the cross and through His Blood shed on the cross to offer those of Israel who believe Salvation. The "seed" is about Christ's seed which Paul just mentioned back at Gal.3:16 which would come through Abraham. That's who the Promise was given to through Abraham at the first per Genesis. The Promise then later went to the Gentiles (along with scattered Israelites of the ten tribes) after the majority of Jews at Jerusalem rejected Christ Jesus.
20 Now a mediator is not a mediator of one, but God is one.
21 Is the law then against the promises of God? God forbid: for if there had been a law given which could have given life, verily righteousness should have been by the law.
22 But the scripture hath concluded all under sin, that the promise by faith of Jesus Christ might be given to them that believe.
But is the law against The Promise by Faith from God? NO. We have ALL been concluded under sin, so that Salvation could ONLY come by Faith on Jesus Christ, and ONLY for those who believe on Jesus Christ by Faith.
23 But before faith came, we were kept under the law, shut up unto the faith which should afterwards be revealed.
Before The Gospel was manifest by Christ's crucifixion, we were only kept under the law unto the Promise by Faith that would later be revealed (Greek apokalupto - made manifest, disclosed). In other words, the only thing involving The Gospel that was manifest prior to Christ's first coming was the Promise by Faith only.
24 Wherefore the law was our schoolmaster to bring us unto Christ, that we might be justified by faith.
25 But after that faith is come, we are no longer under a schoolmaster.
There's what the law was given for, to point towards Christ Jesus when He would come to manifest The Gospel Promise by His crucifixion, defeating death and the devil for us (Hebrews 2:14). We now await the glory of our redemption by Christ at His return. But again, does that mean the law is no more, and of no benefit? No.
26 For ye are all the children of God by faith in Christ Jesus.
27 For as many of you as have been baptized into Christ have put on Christ.
28 There is neither Jew nor Greek, there is neither bond nor free, there is neither male nor female: for ye are all one in Christ Jesus.
29 And if ye be Christ's, then are ye Abraham's seed, and heirs according to the promise.
(KJV)
Regardless of what nation or people one is born of, if they believe The Gospel Promise by Faith like Abraham's Faith, then they are counted as "Abraham's seed". The Promise was first to Abraham, and to his literal flesh seed, and also included the promises to Abraham God gave along with it. The Promise by Faith includes all the other promises from God that began with Abraham. THAT IS WHAT WE GENTILES ARE ALSO 'HEIRS' OF ACCORDING TO THE PROMISE.
This is why we cannot separate God's Promise by Faith first given through Abraham, nor His promises to Abraham's seed apart from Christ's Church. If we Gentiles in Christ Jesus are heirs of the Promise to Abraham, then we are heirs WITH Abraham. That right there is what Paul was teaching in that Galatians 3 chapter with Abraham.
Furthermore, this means Christ's Church INHERITED God's promises with Abraham, especially since The Gospel was refused by the majority of Judah, Benjamin, and Levi in Jerusalem, just as the majority of those STILL refuse The Gospel Promise today!
For those who understand that, this is why it is IMPOSSIBLE to separate God's concept of Israel apart from Christ's Church! Trying to do that would be like trying to separate Abraham from The Promise God first gave through him which he believed by Faith. If it were possible to do that, then it would mean Abraham would no longer be heir, and nor us with him. That's is the ONLY way believers on Christ could not be counted as children of Abraham. This is why those in Christ Jesus need to CLAIM the promises God gave to Abraham and his seed, and start actually believing what Paul said there that we now are inheritors with faithful Abraham.