The logical axiom
 |
where 
denotes NOT and 
denotes OR, that, when taken together
with associativity and commutativity, is equivalent to the axioms of Boolean
algebra.
The Robbins operator can be defined in the Wolfram Language by
Robbins := Function[{x, y}, ! (! (! y \[Or] x)
\[Or] ! (x \[Or] y))]
That the Robbins axiom is a true statement in Boolean algebra can be verified by examining its truth table.
 |  |  |
| T | T | T |
| T | F | T |
| F | T | F |
| F | F | F |
