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http://imageshack.us/m/3/4510/axiomsq.png

which I'm confused about. I know what the axioms of probability are but how would I use them to "derive" that result? I could illustrate why P(A∪B) = P(A) + P(B) - P(A∩B) on a Venn diagram but I have no idea how to use the axioms to show it.