Prove the following implication.......?

Prove this by induction on n. Base case: n = 2. Then x_1 * x_2 = 0 => x_1 = 0 or x_2 = 0. Inductive step: suppose the statement holds for x_1*x_2*...*x_n-1. Then if (x_1*x_2*...*x_n-1)(x_n) = 0, either x_n = 0, or (x_1*...*x_n-1) = 0, in which case our induction hypothesis tells us that x_1 = 0, or x_2 = 0, or ... x_n-1 = 0. So one of the x's is 0.