$2^n<n!$ for some $n>3\in\mathbb Z^+$

Basic step is true with $n=4$.

So induction step assume $2^n<n!$ for some $n>3\in\mathbb Z^+$ is true. 

Will show that $2^{n+1}<(n+1)!$ for some $n>3\in\mathbb Z^+$.

Consider $2^{n+1}=(2)2^n$