let Y be non empty set ; :: thesis: for a, b, c being Element of Funcs (Y,BOOLEAN) holds a 'nor' (b 'nand' c) = (('not' a) '&' b) '&' c
let a, b, c be Element of Funcs (Y,BOOLEAN); :: thesis: a 'nor' (b 'nand' c) = (('not' a) '&' b) '&' c
thus a 'nor' (b 'nand' c) = 'not' (a 'or' (b 'nand' c)) by Th2
.= 'not' (a 'or' ('not' (b '&' c))) by Th1
.= ('not' a) '&' ('not' ('not' (b '&' c))) by BVFUNC_1:13
.= (('not' a) '&' b) '&' c by BVFUNC_1:4 ; :: thesis: verum