I need help proving this theorem using the axioms and theorems shown in the picture: If $n,m$ are in the natural numbers and $n\ge m$ then $n-m$ is in the natural numbers (https://i.stack.imgur.com/I665o.jpg)
- Since $n\geq m$, $n-m\geq 0$.
- Since $n,m$ are both integers (being natural numbers), $n-m$ is also an integer (because the integers are a closed set).
Combining statements $1$ and $2$ says that $n-m$ is a non-negative integer. Therefore it is a natural number.