let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds 'not' (a 'nand' b) = a '&' b
let a, b be Function of Y,BOOLEAN; :: thesis: 'not' (a 'nand' b) = a '&' b
'not' (a 'nand' b) = 'not' ('not' (a '&' b)) by th1;
hence 'not' (a 'nand' b) = a '&' b ; :: thesis: verum