let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds a 'nand' (b '&' c) = (a '&' b) 'nand' c
let a, b, c be Function of Y,BOOLEAN; :: thesis: a 'nand' (b '&' c) = (a '&' b) 'nand' c
(a '&' b) 'nand' c = 'not' ((a '&' b) '&' c) by th1;
hence a 'nand' (b '&' c) = (a '&' b) 'nand' c by Th9; :: thesis: verum