let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds
( a 'nand' (b 'nand' c) = ('not' a) 'or' (b '&' c) & a 'nand' (b 'nand' c) = a 'imp' (b '&' c) )
let a, b, c be Function of Y,BOOLEAN; :: thesis: ( a 'nand' (b 'nand' c) = ('not' a) 'or' (b '&' c) & a 'nand' (b 'nand' c) = a 'imp' (b '&' c) )
a 'nand' (b 'nand' c) = 'not' (a '&' (b 'nand' c)) by th1
.= 'not' (a '&' ('not' (b '&' c))) by th1
.= ('not' a) 'or' ('not' ('not' (b '&' c))) by BVFUNC_1:14
.= ('not' a) 'or' (b '&' c) ;
hence ( a 'nand' (b 'nand' c) = ('not' a) 'or' (b '&' c) & a 'nand' (b 'nand' c) = a 'imp' (b '&' c) ) by BVFUNC_4:8; :: thesis: verum