Why is it hardly relevant? Booleans are, per definition, 0 and 1.
So in BM, Not(not x) IS equal to x for the set of booleans which is {0,1}
Those 2 are the only ones where not is defined as boolean operations so I don't know what your problem is.
(I know that with higher logics this isn't true, but programming languages only know of 0 and 1, not of the other 3 - 6 states that exist in reality. Those operations define not etc through matrices which define what not x is)
So in BM, Not(not x) IS equal to x for the set of booleans which is {0,1}
Those 2 are the only ones where not is defined as boolean operations so I don't know what your problem is.
(I know that with higher logics this isn't true, but programming languages only know of 0 and 1, not of the other 3 - 6 states that exist in reality. Those operations define not etc through matrices which define what not x is)