Minimal axioms for Boolean algebra

In mathematical logic, minimal axioms for Boolean algebra are assumptions which are equivalent to the axioms of Boolean algebra (or propositional calculus), chosen to be as short as possible. For example, an axiom with six NAND operations and three variables is equivalent to Boolean algebra: ( ( a ∣ b ) ∣ c ) ∣ ( a ∣ ( ( a ∣ c ) ∣ a ) ) = c {\displaystyle ((a\mid b)\mid c)\mid (a\mid ((a\mid c)\mid a))=c} where the vertical bar represents the NAND logical operation (also known as the Sheffer stroke).

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