If no $k,l \in \mathbb N$ : $x_1=2^k$ and $x_2=2^l$, in which $x_1$, $x_2$ $\in \mathbb N$, then there is no $m \in \mathbb N$, so that $x_1x_2=2^m$?

Question

How to prove : if there is no natural numbers $k,l$ that $x_1=2^k$ and $x_2=2^l$, in which $x_1, x_2$ are natural numbers, then there is no natural number $m$, so that $x_1x_2=2^m$?

$$x_1 \in N \land x_2 \in N \land (\not \exists k) (k \in N \land x_1=2^k) \land (\not \exists l) (l \in N \land x_2=2^l) \Rightarrow (\not \exists m) (m \in N \land x_1*x_2=2^m) $$