What is the basis for saying that the Antichrist, man of lawlessness, and the beast of Revelation 13 are all the same?

Irenaeus, a disciple of Polycarp who was a disciple of John, gave these reasons in the second century when the apostolic teaching was fresh in the church.

2. And for this reason the apostle says: “Because they received not the love of God, that they might be saved, therefore God shall also send them the operation of error, that they may believe a lie, that they all may be judged who have not believed the truth, but consented to unrighteousness.” [2 Thess. ii. 10–12.] For when he (Antichrist) is come, and of his own accord concentrates in his own person the apostasy, and accomplishes whatever he shall do according to his own will and choice, sitting also in the temple of God, so that his dupes may adore him as the Christ; wherefore also shall he deservedly “be cast into the lake of fire:” [Rev. xix. 20.] [this will happen according to divine appointment], God by His prescience foreseeing all this, and at the proper time sending such a man, “that they may believe a lie, that they all may be judged who did not believe the truth, but consented to unrighteousness;” whose coming John has thus described in the Apocalypse: “And the beast which I had seen was like unto a leopard, and his feet as of a bear, and his mouth as the mouth of a lion; and the dragon conferred his own power upon him, and his throne, and great might. And one of his heads was as it were slain unto death; and his deadly wound was healed, and all the world wondered after the beast. And they worshipped the dragon because he gave power to the beast; and they worshipped the beast, saying, Who is like unto this beast, and who is able to make war with him? And there was given unto him a mouth speaking great things, and blasphemy and power was given to him during forty and two months. And he opened his mouth for blasphemy against God, to blaspheme His name and His tabernacle, and those who dwell in heaven. And power was given him over every tribe, and people, and tongue, and nation. And all who dwell upon the earth worshipped him, [every one] whose name was not written in the book of the Lamb slain from the foundation of the world. If any one have ears, let him hear. If any one shall lead into captivity, he shall go into captivity. If any shall slay with the sword, he must be slain with the sword. Here is the endurance and the faith of the saints.” [Rev. xiii. 2], etc. After this he likewise describes his armour-bearer, whom he also terms a false prophet: “He spake as a dragon, and exercised all the power of the first beast in his sight, and caused the earth, and those that dwell therein, to adore the first beast, whose deadly wound was healed. And he shall perform great wonders, so that he can even cause fire to descend from heaven upon the earth in the sight of men, and he shall lead the inhabitants of the earth astray.” [Rev. xiii. 11, etc.] Let no one imagine that he performs these wonders by divine power, but by the working of magic. And we must not be surprised if, since the demons and apostate spirits are at his service, he through their means performs wonders, by which he leads the inhabitants of the earth astray. John says further: “And he shall order an image of the beast to be made, and he shall give breath to the image, so that the image shall speak; and he shall cause those to be slain who will not adore it.” He says also: “And he will cause a mark [to be put] in the forehead and in the right hand, that no one may be able to buy or sell, unless he who has the mark of the name of the beast or the number of his name; and the number is six hundred and sixty-six,” [Rev. xiii. 14, etc.] that is, six times a hundred, six times ten, and six units. [He gives this] as a summing up of the whole of that apostasy which has taken place during six thousand years. Book V. Chapter XXVIII.—The distinction to be made between the righteous and the wicked. The future apostasy in the time of Antichrist, and the end of the world.