let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds a '&' (b 'nand' c) = (a '&' ('not' b)) 'or' (a '&' ('not' c))
let a, b, c be Function of Y,BOOLEAN; :: thesis: a '&' (b 'nand' c) = (a '&' ('not' b)) 'or' (a '&' ('not' c))
thus a '&' (b 'nand' c) = a '&' ('not' (b '&' c)) by th1
.= a '&' (('not' b) 'or' ('not' c)) by BVFUNC_1:14
.= (a '&' ('not' b)) 'or' (a '&' ('not' c)) by BVFUNC_1:12 ; :: thesis: verum