The meat of Bush's "proof":

The United Nations concluded in 1999 that Saddam Hussein had biological weapons materials sufficient to produce over 25,000 liters of anthrax; enough doses to kill several million people. He hasn't accounted for that material. He has given no evidence that he has destroyed it. The United Nations concluded that Saddam Hussein had materials sufficient to produce more than 38,000 liters of botulinum toxin; enough to subject millions of people to death by respiratory failure. He hasn't accounted for that material. He's given no evidence that he has destroyed it. Our intelligence officials estimate that Saddam Hussein had the materials to produce as much as 500 tons of sarin, mustard and VX nerve agent. In such quantities, these chemical agents could also kill untold thousands. He's not accounted for these materials. He has given no evidence that he has destroyed them. U.S. intelligence indicates that Saddam Hussein had upwards of 30,000 munitions capable of delivering chemical agents. Inspectors recently turned up 16 of them, despite Iraq's recent declaration denying their existence. Saddam Hussein has not accounted for the remaining 29,984 of these prohibited munitions. He has given no evidence that he has destroyed them. From three Iraqi defectors we know that Iraq, in the late 1990s, had several mobile biological weapons labs. These are designed to produce germ warfare agents and can be moved from place to a place to evade inspectors. Saddam Hussein has not disclosed these facilities. He has given no evidence that he has destroyed them. The International Atomic Energy Agency confirmed in the 1990s that Saddam Hussein had an advanced nuclear weapons development program, had a design for a nuclear weapon and was working on five different methods of enriching uranium for a bomb. The British government has learned that Saddam Hussein recently sought significant quantities of uranium from Africa. Our intelligence sources tell us that he has attempted to purchase high-strength aluminum tubes suitable for nuclear weapons production.

Notice the clever obfuscation in the comment about the aluminum tubes. Bush gets around the inconvenient fact that there is no evidence that they are being used for "nuclear weapons production" by asserting the undisputed claim that they have "attempted to purchase" them and then leave it as an exercise to the listener to conclude that the only reason this was done was for "nuclear weapons production".