let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds a 'nor' (b 'nand' c) = 'not' ((a 'or' ('not' b)) 'or' ('not' c))
let a, b, c be Function of Y,BOOLEAN; :: thesis: a 'nor' (b 'nand' c) = 'not' ((a 'or' ('not' b)) 'or' ('not' c))
thus a 'nor' (b 'nand' c) = a 'nor' ('not' (b '&' c)) by th1
.= 'not' (a 'or' ('not' (b '&' c))) by Th2
.= 'not' (a 'or' (('not' b) 'or' ('not' c))) by BVFUNC_1:14
.= 'not' ((a 'or' ('not' b)) 'or' ('not' c)) by BVFUNC_1:8 ; :: thesis: verum