Many years ago, a math teacher of mine thought us that there was a mathematical symbol for "that is" / "to clarify" / "whereby" (I'm not from an English speaking country, so I'm writing several alternatives here to try to approximate the actual meaning that I was thought), which looked a bit like: "$\supset :$" (or rather, a backwards capital C (alternatively an open o; the symbol was handwritten, so hard to tell) followed by a colon, but I don't know how to write that here).
As for usage, my teacher used it when doing algebra when she wanted to skip a few lines (hence, I suppose you could take it to mean "one sees easily that", but that's not how she "translated" the symbol), as in:
\begin{align}
&6x + 2 = 20 \\
\supset: \quad &x= 3,
\end{align}
(this being an overly simple example), or when she wanted to re-state the conclusion of an algebraic derivation using slightly different notation which better reflected whatever it was that she wanted us to take away from said derivation, as in:
\begin{align}
&6x + 2 = 20 \\
&\quad \vdots \\
& x = 3 \\
\supset: \quad &x= \sqrt{9},
\end{align}
(this still being an overly simple example, and possibly a somewhat silly one).
However, I haven't been able to find anything on the web confirming the existence of this symbol, and my question is therefore: Have anyone else seen anything like this?
As for the the necessity of this symbol, I do realize that this symbol is rather redundant, since one might as well use "$\implies$", "$\iff$", simply some text, or possibly (in some cases) even "$\therefore$".
Best Answer
It's not a symbol, but the abbreviation "i.e." is short for the Latin phrase id est which is typically translated as "that is." The abbreviation is very commonly used for this meaning in math.