Often in lectures when the lecturer proves a statement , $A \iff B$, they start off with writing ("$\Longrightarrow$") then proceeds to prove that $B$ follows from $A$ and then, ("$\Longleftarrow$") for the opposite. I understand this is usually for clarity during the lectures, but I was wondering if this was also a common practice within mathematical writing? A similar thing can be said for set equalities that is I often see ("$\subset$") and ("$\supset$"), sometimes without parenthesis.
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2I don't see this very often in papers (though I am sure that I have seen it once or twice), but I doubt that anyone is going to stop you if you include it. I also don't really think that this is on-topic here---really, this is a discussion that you should have with your advisor (assuming that you are writing a thesis of some sort), or the editor of whatever journal you are submitting your paper to. – Xander Henderson Feb 24 '21 at 13:07
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Oh sorry didn't realise this was off topic, I just saw other questions talking about formality in proof writing so I thought it was okay, I can delete it if prompted to. On another note, I was just curious and not currently writing any paper (still in my second year). – ASP Feb 24 '21 at 13:15
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1It is rare that an "if and only if" proof can be made just using $\iff$ equivalences. The rule is more often that the "if" and the "ony if" parts are proven separately. – Feb 24 '21 at 13:33