Two propositions are equivalent if they are both true. Closed form of 2th. Equivalent to a biimp -like version of the xor-connective. This theorem stays true, no matter how you permute its operands. This is evident from its sharper version \( \varphi \leftrightarrow (\psi \leftrightarrow (\varphi \leftrightarrow \psi)) \). (Contributed by Wolf Lammen, 12-May-2013.)