Equivalences & Rewrite Rules:
If notice that as well as allowing us to prove trivial theorems, and tautologies enable us to establish that certain sentences are saying the same thing. In fact there is particularly, if we can show that A↔B is a tautology about we know A and B are true for exactly the same models, that is identical columns in a truth table but if we say like if A and B are logically equivalent, than to written as the equivalence A≡B. There is clearly and signify the same thing here, that why use two different symbols? Because it's a technical difference: A↔B is a sentence of propositional logic, thatwherever A≡ B is a claim we make outside the logic mostly.
In fact like a language, that we could replace the phrase is "There's only one Tony Blair" through "Tony Blair is unique", but there in sentences, we see that basically the phrases mean the same thing but probably we can do exactly the same in logical languages, like an advantage: is just because we are being more formal, than we will have mathematically proved such two sentences are corresponding. Because it means that there is extremely no situation in that one sentence would be interpreted in a different way to another, that is certainly probable with natural language sentences just about Tony Blair.