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When writing little proofs to write a larger one, I often try to make a chain of $\iff,$ to get to an obviously true statement. I feel like it would be nice to do just another $\iff$ to an symbol that stands for "true statement," a boolean constant, if you like. Is there such a thing?

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You can use $\top$ for true and $\bot$ for false.

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Note that I'm not going to provide such a symbol, but rather argue that it shouldn't be introduced in the first place.

Something is never simply "true" without context. A statement can be true if another statement that implies the first statement is considered true, which is again only true if it is implied by a third true statement, etc. This chain in principle goes all the way down to the axioms of your theory.

In practice, however, one often stops (or starts) a proof at some well-known assertion. But introducing a whole symbol for just that part would probably just be confusing; instead, you should explain (with words) why that assertion should be considered true, or give some reference.

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    Ok, I was thinking of a statement like 1=1, which I can assume is true without context in the environment I practice math at the moment. In principle, I could imagine that you are right and some quite philosophical implications might arise from your argument. – 2017-02-26
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    Let's say you arrive at a statements like $1=1$ in your proof. Then my point is that you should simply write, "which is obviously true, so we can conclude that ..." and not write some symbol next to it. It is a common trap for people entering more rigorous/proof-based math to think that more symbols means more formal means better. However, the goal of any proof is to convey some mathematical truth as *clearly as possible*. Obscure and specialized notation almost always hinders this; better to write it with words instead. Does this address your concern, or have I misunderstood? – 2017-02-26
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    I don't think a symbol meaning 'true' or 'which is clearly true' is all that specialised. There is a symbol which denotes a contradiction (※), which can be used to say that a statement is obviously untrue. I also think that English isn't necessarily more clear than math notation. If saying "which is obviously true" is fine, there's no reason why a widely understood symbol meaning the same thing, is not fine. Everything has and needs a context, especially normal language. Yes, if you would be resorting to an obscure, unknown symbol, that would obviously be inadvisable. – 2017-10-15
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    @lukeuser The problem, as I see it, is that no such widely recognized symbols exist, so you'd have to explain it with words anyway, and at that point, it simply becomes redundant to introduce the symbols. – 2017-10-15