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Is there a formal definition of the $\because$ (because) symbol? If so, what is it?

I use (or abuse?) the $\because$ symbol to introduce assumptions, definitions, or to other assertions. I first encountered it in a formal logic course in which the professor openly bragged about not using it in a strictly correct way.

I am adding a screen scrape of what I was working on when I asked the question. These are personal notes with a target audience consisting of the author. I decided to attempt an explanation that I might give to another reader if such a mythical creature were to exist. The particular statement captures a number of my notational idiosyncratices, so it seemed like a good subject.

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Steven Thomas Hatton
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    compare https://math.stackexchange.com/q/921396/42969 or https://math.stackexchange.com/q/2231664/42969 – Martin R Dec 13 '21 at 10:42
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    My advice: in material to be read by others, do not use $\because$, but instead write words (like "since"). – GEdgar Dec 13 '21 at 11:23
  • Neither of the referenced questions have satisfying answers. Perhaps $\because$ (because) means 'because' is the best I can hope for. – Steven Thomas Hatton Dec 13 '21 at 11:23
  • @GEdgar using word kind of defeats the whole "symbolic" part of symbolic logic. The $\because$ symbol may not be logically necessary, but it is convenient. – Steven Thomas Hatton Dec 13 '21 at 11:46
  • @mauro you closed this as a duplucate, but this question is about the "because" symbol and the other question does not have any answers that mention that. I am voting to reopen. – MJD Dec 13 '21 at 12:58
  • @steven I have never actually seen this used, and I wonder if it fell out of general use even before the beginning of mathematical logic in the late 19th century. In which case there would not be any formal definition, beyond "it is an abbreviation of 'because'". The use in your example is not standard. – MJD Dec 13 '21 at 13:01
  • No "because" symbol in logic. – Mauro ALLEGRANZA Dec 13 '21 at 13:04
  • Have you seen this post? – Mauro ALLEGRANZA Dec 13 '21 at 13:05
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    @Steven: These symbols are only convenient for the few people who use them. For most people who read mathematics as humans, this symbol is just another thing you need to look up online or try and figure out from the context. – Asaf Karagila Dec 13 '21 at 13:05
  • IMO, what you are writing is simply: "if $[ A \land B \to C]$, then $D \land E$" that can also be written as $[ A \land B \to C] \therefore D \land E$ – Mauro ALLEGRANZA Dec 13 '21 at 13:08
  • @MauroALLEGRANZA $[ A \land B \to C] \therefore D \land E$ is a good idea. I will take it under advisement. – Steven Thomas Hatton Dec 13 '21 at 16:57

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