let Y be non empty set ; :: thesis: for a, b, c being Element of Funcs (Y,BOOLEAN) holds a 'nand' (b 'imp' c) = (('not' a) 'or' b) '&' ('not' (a '&' c))
let a, b, c be Element of Funcs (Y,BOOLEAN); :: thesis: a 'nand' (b 'imp' c) = (('not' a) 'or' b) '&' ('not' (a '&' c))
thus a 'nand' (b 'imp' c) = 'not' (a '&' (b 'imp' c)) by Th1
.= 'not' (a '&' (('not' b) 'or' c)) by BVFUNC_4:8
.= 'not' ((a '&' ('not' b)) 'or' (a '&' c)) by BVFUNC_1:15
.= ('not' (a '&' ('not' b))) '&' ('not' (a '&' c)) by BVFUNC_1:16
.= (('not' a) 'or' ('not' ('not' b))) '&' ('not' (a '&' c)) by BVFUNC_1:17
.= (('not' a) 'or' b) '&' ('not' (a '&' c)) ; :: thesis: verum