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