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**bryangoodrich** However, I fail to see how this represents A is a subset of the power set of A. In fact, it is just not true that A is a subset of the power set of A. Take a simple counter example. Let A = {1, 2}. Let 0 denote the empty set. Then the power set of A is {0, {1}, {2}, A}. Now it is true that A is in the power set of A, but to be a subset of it A must contain something of the power set. In this case, that would be like saying A = {1, 2, {1}} or A = {1, 2, A} or {1, 2, {}} = {1, 2, 0}. Therefore, it is not true. Both the antecedent and the consequent of that implication are false. However, classically this entails that it is a valid material conditional because a false antecedent makes it vacuously true.