Exponent Not Equal to Zero

Theorem
Let $x$ and $y$ be ordinals.

Suppose $x \ne 0$.

Then:


 * $x^y \ne 0$

Proof
The proof shall proceed by Transfinite Induction on $y$.

Basis for the Induction
This proves the basis for the induction.

Induction Step
This proves the induction step.

Limit Case
This proves the limit case.