Here's your irreducible complexity of a mousetrap argument deconstructed in three minutesNope. Basically, irreducible complexity means it is impossible to reduce the complexity of a complex system by removing any of its parts and still maintain its functionality. The common mousetrap illustrates irreducible complexity. It's made of five integral parts: a catch, a spring, a hammer, a holding bar and a foundation. Remove any of them and the design fails. It is complexity that cannot be reduced or simplified.
Incidentally, this is why the argument for irreducible complexity doesn't win converts from the evidence based community. Just because you can't imagine functionality in less complex forms doesn't mean that they can't have function, perhaps of a very different nature than the larger mechanism, or that this function couldn't have been selected by nature by virtue of it conferring a competitive advantage.
You really can't look at a natural mechanism and declare it irreducibly complex just because you can't imagine a slightly less complex mechanism with functionality. Many systems have been offered as examples of irreducible complexity only to have it shown that there was functionality in slightly less complex systems. Famous examples apart from the mousetrap include the flagellar motor on some microorganisms, the coagulation cascade, and the eye.
Also, consider this arch:
You can't remove any segment of the arch without the whole thing coming down. Does this mean that it was intelligently designed and constructed?