Biconditional is Transitive

Theorem

The biconditional operator is transitive:

Formulation 1

$p \iff q, q \iff r \vdash p \iff r$

Formulation 2

$\vdash \paren {\paren {p \iff q} \land \paren {q \iff r} } \implies \paren {p \iff r}$