“And I will strengthen the arms of the king of Babylon, and put my sword in his hand, but I will break the arms of Pharaoh and he will groan before him with the groanings of a deadly wounded man. And I will hold up the arms of the king of Babylon and the arms of Pharaoh will fall down, and they will know that I am Yahweh when I put my sword into the hand of the king of Babylon and he stretches it out on the land of Egypt.”
The success and failure of each side is in the hands of Yahweh. The one whom He strengthens will succeed, the one whom He prevents will fail. Thus because He would make the arms of the king of Babylon strong, and it was His sword that he would bear, the king of Babylon would succeed. And because he would ‘break the arms' of Pharaoh, Pharaoh would be defeated and groan like a mortally wounded man.
The holding up of the arms can be compared with Exodus 17:11-12. The holding up of the arms resulted in victory and here it is Yahweh who would hold up the arms of the king of Babylon so that he won, and vice versa for Egypt.
‘And they will know that I am Yahweh when I put my sword into the hand of the king of Babylon and he stretches it out on the land of Egypt.' Again the purpose of all this was so that Yahweh's power and being may be revealed. The idea is not that men would necessarily recognise Yahweh, but that they would have to accept the evidence of His power. Even if they did not acknowledge it, they would know it in experience.
The fact that Nebuchadnezzar would bear the sword of Yahweh emphasises that he was acting as Yahweh's servant on Yahweh's mission.