A uniquely complemented lattice is a complemented lattice 
that satisfies
![( forall x in L)( forall y in L)[(x ^ y=0) ^ (x v y=1)]=>y=x^'.](/images/equations/UniquelyComplementedLattice/NumberedEquation1.svg) |
The class of uniquely complemented lattices is not a subvariety of the class of complemented lattices. On the other hand, there is a well-known class of uniquely complemented lattices that is a subvariety of the variety of complemented lattices, namely the class of Boolean algebras. They form a variety because they are the distributive complemented lattices, and one can prove that any distributive complemented lattice is uniquely complemented.
