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
This is demonstrated in Functionally Complete Logical Connectives‎.

It is documented here as a separate page because of its historical and scientific significance.

History
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 till 1933.