Acts 13 says clearly,
48 Now when the Gentiles heard this, they were glad and glorified the word of the Lord.
And as many as had been appointed to eternal life believed.
The appointment by God to their eternal life came before their belief in Christ, that is what predestination means, chosen by the Father to be given to Christ as His children, in the future. This was decided from the beginning of all things. Only those so appointed by God believed the message of the gospel, and gained eternal life in Christ, and the rest were hardened...
Those appointed are the elect.
Romans 11, God does not cast away His people whom HE FOREKNEW, God saves them.
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1
I say then, has God cast away His people? Certainly not! For I also am an Israelite, of the seed of Abraham,
of the tribe of Benjamin. 2 God has not cast away His people whom He foreknew. Or do you not know what the Scripture says of Elijah, how he pleads with God against Israel, saying, 3 “Lord, they have killed Your prophets and torn down Your altars, and I alone am left, and they seek my life”? 4 But what does the divine response say to him?
“I have reserved for Myself seven thousand men who have not bowed the knee to Baal.” 5 Even so then, at this present time there is a remnant according to the election of grace. 6 And if by grace, then
it is no longer of works; otherwise grace is no longer grace. [
a]But if
it is of works, it is no longer grace; otherwise work is no longer work.
7 What then? Israel has not obtained what it seeks;
but the elect have obtained it, and the rest were blinded. 8 Just as it is written:
“God has given them a spirit of stupor,
Eyes that they should not see
And ears that they should not hear,
To this very day.”
9 And David says:
“Let their table become a snare and a trap,
A stumbling block and a recompense to them.
10 Let their eyes be darkened, so that they do not see,
And bow down their back always.”
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Acts 13
44 On the next Sabbath almost the whole city came together to hear the word of God. 45 But when the Jews saw the multitudes, they were filled with envy; and contradicting and blaspheming, they opposed the things spoken by Paul. 46 Then Paul and Barnabas grew bold and said, “It was necessary that the word of God should be spoken to you first; but since you reject it, and judge yourselves unworthy of everlasting life, behold, we turn to the Gentiles. 47 For so the Lord has commanded us:
‘I have set you as a light to the Gentiles,
That you should be for salvation to the ends of the earth.’ ”
48 Now when the Gentiles heard this, they were glad and glorified the word of the Lord. And as many as had been appointed to eternal life believed.
49 And the word of the Lord was being spread throughout all the region. 50 But the Jews stirred up the devout and prominent women and the chief men of the city, raised up persecution against Paul and Barnabas, and expelled them from their region. 51 But they shook off the dust from their feet against them, and came to Iconium. 52 And the disciples were filled with joy and with the Holy Spirit.