The second statement is not a corollary of the first one, because “X is necessary for Y” (or “if Y, then X”) does not imply “X is sufficient for Y” (or “if X, then Y”).
The second statement is not a corollary of the first one, because “X is necessary for Y” (or “if Y, then X”) does not imply “X is sufficient for Y” (or “if X, then Y”).