Biconditional in terms of NAND

Theorem

 * $p \iff q \dashv \vdash \left({\left({p \uparrow q}\right) \uparrow \left({p \uparrow q}\right)}\right) \lor \left({\left({\left({p \uparrow p}\right) \uparrow \left({q \uparrow q}\right)}\right) \uparrow \left({\left({p \uparrow p}\right) \uparrow \left({q \uparrow q}\right)}\right)}\right)$

where $\iff$ denotes logical biconditional and $\uparrow$ denotes logical NAND.