as though there was something double about "everything promised to the fathers is fulfilled for you their children in the resurrection of Jesus."
Matthew 22:23 The same day came to him the Sadducees, which say that there is no resurrection, and asked him,
Matthew 22:28 Therefore in the resurrection whose wife shall she be of the seven? for they all had her.
Matthew 22:30 For in the resurrection they neither marry, nor are given in marriage, but are as the angels of God in heaven.
Matthew 22:31 But as touching the resurrection of the dead, have ye not read that which was spoken unto you by God, saying,
Luke 14:14 And thou shalt be blessed; for they cannot recompense thee: for thou shalt be recompensed at the resurrection of the just.
Luke 20:36 Neither can they die any more: for they are equal unto the angels; and are the children of God, being the children of the resurrection.
John 11:24 Martha saith unto him, I know that he shall rise again in the resurrection at the last day.
John 11:25 Jesus said unto her, I am the resurrection, and the life: he that believeth in me, though he were dead, yet shall he live:
This in Acts 13 is about that promise...
Acts 13:32 And we declare unto you glad tidings, how that the promise which was made unto the fathers, 13:33 God hath fulfilled the same unto us their children, in that he hath raised up Jesus again; as it is also written in the second psalm, Thou art my Son, this day have I begotten thee. 13:34 And as concerning that he raised him up from the dead, now no more to return to corruption, he said on this wise, I will give you the sure mercies of David. 13:35 Wherefore he saith also in another psalm, Thou shalt not suffer thine Holy One to see corruption. 13:36 For David, after he had served his own generation by the will of God, fell on sleep, and was laid unto his fathers, and saw corruption: 13:37 But he, whom God raised again, saw no corruption.
Who qualifies for this promise?
13:38 Be it known unto you therefore, men and brethren, that through this man is preached unto you the forgiveness of sins: 13:39 And by him all that believe are justified from all things, from which ye could not be justified by the law of Moses.
Paul's repeat of this resurrection promise...
Acts 23:6 But when Paul perceived that the one part were Sadducees, and the other Pharisees, he cried out in the council, Men and brethren, I am a Pharisee, the son of a Pharisee: of the hope and resurrection of the dead I am called in question.
Acts 24:15 And have hope toward God, which they themselves also allow, that there shall be a resurrection of the dead, both of the just and unjust.
Acts 26:6 And now I stand and am judged for the hope of the promise made of God unto our fathers: 26:7 Unto which promise our twelve tribes, instantly serving God day and night, hope to come. For which hope's sake, king Agrippa, I am accused of the Jews. 26:8 Why should it be thought a thing incredible with you, that God should raise the dead?
That is what one first proves to a Jew...about Christ...to this...very...day.
And that is what one first proves to a Gentile as well.
1 Corinthians 15:1 Moreover, brethren, I declare unto you the gospel which I preached unto you, which also ye have received, and wherein ye stand; 15:2 By which also ye are saved, if ye keep in memory what I preached unto you, unless ye have believed in vain. 15:3 For I delivered unto you first of all that which I also received, how that Christ died for our sins according to the scriptures; 15:4 And that he was buried, and that he rose again the third day according to the scriptures:
Verse 2's "unless ye have believed in vain" - what meaneth that?
1 Corinthians 15:12 Now if Christ be preached that he rose from the dead, how say some among you that there is no resurrection of the dead? 15:13 But if there be no resurrection of the dead, then is Christ not risen: 15:14
And if Christ be not risen, then is our preaching vain, and your faith is also vain. 15:15 Yea, and we are found false witnesses of God; because we have testified of God that he raised up Christ: whom he raised not up, if so be that the dead rise not. 15:16 For if the dead rise not, then is not Christ raised: 15:17 And if Christ be not raised, your faith is vain; ye are yet in your sins. 15:18 Then they also which are fallen asleep in Christ are perished. 15:19 If in this life only we have hope in Christ, we are of all men most miserable. 15:20 But now is Christ risen from the dead, and become the firstfruits of them that slept.
Acts 13 is merely asserting the Resurrection and who gets to be a part of it.