Proof of Theorem NME7

Theorem SMZD says $A$ is singular if and only if $\detname{A}=0$. If we negate each of these statements, we arrive at two contrapositives that we can combine as the equivalence, $A$ is nonsingular if and only if $\detname{A}\neq 0$. This allows us to add a new statement to the list found in Theorem NME6.