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It meets the terms of the UN charter so no UN resolution was needed
However, the US government stated that an armed attack by Iraq did occur against the US and its coalition partners as demonstrated by the assassination attempt on former US President George H. W. Bush in 1993 and firing on coalition aircraft enforcing the no-fly zones over Northern and Southern Iraq since the 1991 Gulf War ceasefire agreement. Under Article 51 of the UN Charter, the US reserved the right to self-defense, even without a UN mandate, as were the cases in the bombing of Iraq in June 1993 in retaliation for Hussein's attempt on former President Bush's life and again in 1996 in retaliation for Hussein's targeting of American aircraft patrolling the no-fly zones over Northern and Southern Iraq and the launching of a major offensive against the city of Irbil in Iraqi Kurdistan in violation of UNSC Resolution 688 prohibiting repression of Iraq's ethnic minorities.[12][13]
Um, yeah, we really needed to defend ourselves from a guy whose authority barely extended beyond Baghdad at that point.
Puh-lease.
Still shows that you are wrong though doesn't it, and that under the terms of the UN charter the second war was legal. The first war was as a result of a UN resolution so again was legal.