Duplicating the method of proof of Theorem 2.10, show that P(A B C D)

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Duplicating the method of proof of Theorem 2.10, show that P(A ∩ B ∩ C ∪ D) = P(A) · P(B| A) · P(C| A ∩ B) · P(D| A ∩ B ∩ C) provided that P(A ∩ B ∩ C) ≠ 0.
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