NAND and NOR are Functionally Complete

Theorem
The NAND and NOR operators are each functionally complete.

That is, NAND and NOR are Sheffer operators.

Proof
In NAND is Functionally Complete it is demonstrated that NAND is functionally complete.

In NOR is Functionally Complete it is demonstrated that NOR is functionally complete.

History
This result is documented separately here because of its historical and scientific significance.

It was proved in 1913 by Henry Sheffer, after whom the symbol $\uparrow$, the Sheffer stroke, is named after.

However, it later transpired that Charles Sanders Peirce had noticed the same result in 1880, but the paper in which this appeared was not published until 1933.