In schools, many students learn the usage of "$\therefore$" and "$\because$" in proofs. Such three-dot notation are popular in many high-school books and exams, but are almost never used in university-level texts. (It seems that, at degree level, this notation only appears in some books about mathematical logic.)
Very often, it is somewhat awkward to use "$\therefore$" and "$\because$" for proofs, because modus ponens, the most commonly used principle of deduction, contains three parts, while "$\therefore$" and "$\because$" are just two symbols. Modus ponens states that from $A\Rightarrow B$ and $A$ we could deduce $B$, so the three parts are: $A\Rightarrow B$, $A$ and $B$.
We will of course write $B$ after "$\therefore$", but it is a good question where to put $A\Rightarrow B$ and $A$. We may either put both $A$ and $A\Rightarrow B$ after "$\because$", or put $A$ after "$\because$" and $A\Rightarrow B$ in brackets after "$\therefore B$".
In the end, the three-dot notation does not make the logic structure entirely clear. "$\therefore $" clearly indicates the conclusion, but the meaning of "$\because$" is not entirely clear - it could be either a theorem $A\Rightarrow B$ or a condition $A$. Sometimes, $A$ is too long (takes too many words) to be written out fully, which causes confusion.
Is there any better alternative to the three-dot notation? It is, after all, completely clear to just write everything in words.