Quantifier/Examples/Existence of x^y = y^x

Example of Use of Quantifiers
Let $x$ and $y$ be in the natural numbers.


 * $\exists x: \exists y: \paren {x \ne y} \land x^y = y^z$

means:


 * There exist natural numbers $x$ and $y$ such that $x^y$ equals $y^x$.

This is true:
 * $2^4 = 16 = 4^2$