let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds a 'xor' (b 'nand' c) = (('not' a) '&' ('not' (b '&' c))) 'or' ((a '&' b) '&' c)
let a, b, c be Function of Y,BOOLEAN; :: thesis: a 'xor' (b 'nand' c) = (('not' a) '&' ('not' (b '&' c))) 'or' ((a '&' b) '&' c)
thus a 'xor' (b 'nand' c) = a 'xor' ('not' (b '&' c)) by th1
.= (('not' a) '&' ('not' (b '&' c))) 'or' (a '&' ('not' ('not' (b '&' c)))) by BVFUNC_4:9
.= (('not' a) '&' ('not' (b '&' c))) 'or' ((a '&' b) '&' c) by BVFUNC_1:4 ; :: thesis: verum