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Proposition: Limit of a Function is Unique If It Exists
Let $D\subseteq\mathbb R$ be a subset of real numbers and let $f:D\to\mathbb R$ be a function having the limit $L$ at $x=a\in D$. Then this limit is unique. Formally $$\lim_{x\to a} f(x)=L\wedge \lim_{x\to a} f(x)=M\Longrightarrow L=M.$$
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Proofs: 1
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References
Bibliography
 Kane, Jonathan: "Writing Proofs in Analysis", Springer, 2016