let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds 'not' ((a 'or' b) 'or' c) = (('not' a) '&' ('not' b)) '&' ('not' c)
let a, b, c be Function of Y,BOOLEAN; :: thesis: 'not' ((a 'or' b) 'or' c) = (('not' a) '&' ('not' b)) '&' ('not' c)
'not' ((a 'or' b) 'or' c) = ('not' (a 'or' b)) '&' ('not' c) by BVFUNC_1:13
.= (('not' a) '&' ('not' b)) '&' ('not' c) by BVFUNC_1:13 ;
hence 'not' ((a 'or' b) 'or' c) = (('not' a) '&' ('not' b)) '&' ('not' c) ; :: thesis: verum