Prove:
If generalized Cantor hypothesis holds, then for all sets $X$ and $Y$, from
$\vert X\vert < \vert Y \vert$ follows $\vert \mathcal{P}(X)\vert < \vert \mathcal{P}(Y) \vert$.
Generalized Cantor hypothesis:
There do not exist such infinite sets $A$ and $B$, for which would hold $\vert A \vert <\vert B \vert < \vert \mathcal{P}(A) \vert.$
I am not sure what exactly I should do here, because it look like it obviously follows from Cantor's theorem, but that is probably not right.