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In Milnor and Stasheff, it is taken as part of the first axiom that all Stiefel-Whitney classes of a bundle vanish in dimensions greater than the rank of the bundle. However, in other sources this is omitted. The wikipedia article makes it seem like this is actually a result of the axioms. Is there a simple proof of this (the axioms I am using are those listed here http://en.wikipedia.org/wiki/Stiefel%E2%80%93Whitney_class#Axioms)?

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