Acts 13:48 And when the Gentiles heard this, they were glad, and glorified the word of the Lord: and as many as were ordained to eternal life believed.
What it does not say? – It doesn’t say that God chooses or has chosen certain people to believe.
What it does say? – Instead, it simply states the fact that those who have eternal life (those ordained/appointed to eternal life) are the same ones that believed. In other words, those who believed are the same ones who have eternal life. That’s true! Certainly, those people who don’t believe are the ones that don’t have eternal life. But, God does not choose certain people to believe.
In context, we must look at Acts 13:38,39. Paul here is telling us the gospel. He is saying that through this “Man, Jesus Christ, is preached unto you (speaking to Jews and Gentiles) the forgiveness of sins.” All of the world’s sins have been paid for by the death of Christ on the cross. 2 Cor. 5:19 tells us that “God was in Christ reconciling the world unto Himself, not imputing [not counting] their trespasses [sins] against them.” This doesn’t mean that everybody is saved yet. They still need to be declared righteous. Having righteousness is the same as having eternal life.
Rom. 3:22a says, “even the righteousness of God, through faith of Jesus Christ, to all and on all who believe.” The gospel (free gift of eternal life or righteousness) is offered to all, but it is only on all (conferred upon/granted to/awarded to) those who believe. What is that they have to believe? They need to believe that the Lord Jesus Christ died for all of their sins, was buried, and rose again the third day (1 Cor. 15:3,4).
Now come back to Acts 13:39. “And by Him (Christ) everyone who believes is justified from all things from which you could not be justified by the law of Moses.” Again, it’s only those people who believe that it is talking about. And out of those that believe, everyone of them is justified or declared righteous.
So, their is an elect group, who are the saved (it’s made up of believers). But, that doesn’t mean that God has chosen who those people are. They weren’t elected to be saved. He has offered salvation to all of mankind. Anyone can believe the gospel. And out of all the people that do believe, every single one of them are justified from all things. All those that believe are “made the righteousness of God in Him” (2 Cor. 5:20).
So, (getting back to the verse) as many as are ordained to eternal life, those people are the ones that believed the gospel. In conclusion, it does not prove Calvinism.
For more reading material on Calvinism, check out The Power of God unto Salvation: Is the Gospel Enough? by Joel Finck