VII. The rest of mankind God was pleased, according to the unsearchable counsel of His own will, whereby He extends or withholds mercy, as He pleases, for the glory of His sovereign power over His creatures, to pass by; and to ordain them to dishonor and wrath for their sin, to the praised of His glorious justice.How do we know this? Well, first off it follows logically. If God chooses some before the foundation of the world, God must also be rejecting the rest before the foundation of the world. It isn't as if he chooses some and then decides to let the rest figure out where they're going on their own. He knows all things about all people, and his selection of some necessarily entail the rejection of the rest.
But of course "where's the Scripture?" Well, let's go back to Romans 9.
Before they had done anything good or bad, not because of works, God loved Jacob and hated Esau. All this was done in order that "God's purpose of election might continue."
10 And not only so, but also when Rebekah had conceived children by one man, our forefather Isaac, 11 though they were not yet born and had done nothing either good or bad—in order that God's purpose of election might continue, not because of works but because of him who calls— 12 she was told, “The older will serve the younger.” 13 As it is written, “Jacob I loved, but Esau I hated.”Paul continues right after that bold claim to respond to the common objection that we as fallen humans often have, "But this is not fair on God's part." He turns and says that it is God's will whether to have mercy or not, and He can choose to have mercy or he can choose to harden, all in accordance to His free will. It does not depend upon human will or exertion, but upon God who has mercy.
14 What shall we say then? Is there injustice on God's part? By no means! 15 For he says to Moses, “I will have mercy on whom I have mercy, and I will have compassion on whom I have compassion.” 16 So then it depends not on human will or exertion,  but on God, who has mercy. 17 For the Scripture says to Pharaoh, “For this very purpose I have raised you up, that I might show my power in you, and that my name might be proclaimed in all the earth.” 18 So then he has mercy on whomever he wills, and he hardens whomever he wills.Why does God do this? Why does God prepare some for mercy and others for destruction and wrath? (notice it doesn't say that some are prepared for mercy and others prepare themselves) One reason God does this is for the manifestation of His own glory to those He has chosen: "desiring to show his wrath and to make known his power...in order to make known the riches of his glory for vessels of mercy."
19 You will say to me then, “Why does he still find fault? For who can resist his will?” 20 But who are you, O man, to answer back to God? Will what is molded say to its molder, “Why have you made me like this?” 21 Has the potter no right over the clay, to make out of the same lump one vessel for honorable use and another for dishonorable use? 22 What if God, desiring to show his wrath and to make known his power, has endured with much patience vessels of wrath prepared for destruction, 23 in order to make known the riches of his glory for vessels of mercy, which he has prepared beforehand for glory— 24 even us whom he has called, not from the Jews only but also from the Gentiles?God created vessels for destruction so that we, the elect, may know His justice, His wrath, and His mercy, all to the praise of His glorious grace. He has mercy on whom He'll have mercy and He hardens whom He'll harden, all for His glory and to His praise.
See also: Hell is not a place where God is not.