let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds a 'nand' (b '&' c) = 'not' ((a '&' b) '&' c)
let a, b, c be Function of Y,BOOLEAN; :: thesis: a 'nand' (b '&' c) = 'not' ((a '&' b) '&' c)
a 'nand' (b '&' c) = 'not' (a '&' (b '&' c)) by th1;
hence a 'nand' (b '&' c) = 'not' ((a '&' b) '&' c) by BVFUNC_1:4; :: thesis: verum