Unique Limits Proof

Let $L_1,L_2,c\in R$. Suppose that $f$ is defined on an open interval around $c$ (except possibly at $c$) if ${\lim }_{x\to c}=L_1$ and ${\lim }_{x\to c}f(x)=L_2$ then $L_1=L_2$.

Proof

Proof By Contradiction