Functionally Complete Logical Connectives/NOR

Theorem
The singleton set containing the following logical connective:
 * $\left\{{\uparrow}\right\}$: NAND

is functionally complete.

Proof
From Functionally Complete Logical Connectives: Negation and Disjunction, any boolean expression can be expressed in terms of $\lor$ and $\neg$.

From NOR with Equal Arguments:
 * $\neg p \dashv \vdash p \downarrow p$

From Disjunction in terms of NOR:
 * $p \lor q \dashv \vdash \left({p \downarrow q}\right) \downarrow \left({p \downarrow q}\right)$

demonstrating that $p \lor q$ can be represented solely in terms of $\downarrow$.

That is, $\left\{{\downarrow}\right\}$ is functionally complete.

Also see

 * Functionally Complete Logical Connectives/NAND