The following statement cannot be proven in $\mathsf{ZFC}$:

(S) : If $A, B$ are sets with $|A| < |B|$, then $2^{|A|} = |{\cal P}(A)| < |{\cal P}(B)| = 2^{|B|}$.

Obviously, $\mathsf{GCH}$ implies (S). Does (S) imply $\mathsf{GCH}$ too?