let Y be non empty set ; :: thesis: for a, b, c being Element of Funcs Y,BOOLEAN holds a 'nand' (b '&' c) = (a '&' b) 'nand' c
let a, b, c be Element of Funcs 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