We give the definition of well-formed formulas in propositional logic 
using a grammar in Backus-Naur form (BNF) as:
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$$\varphi \coloneqq ~ < \text{atomic proposition>} ~ | ~\varphi \wedge \varphi~ |~ \varphi \vee \varphi~ | ~\neg \varphi ~| ~\varphi \imp \varphi~ | ~\varphi \leftrightarrow \varphi~ | ~( \varphi )$$