let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds a 'nor' (b '&' c) = ('not' (a 'or' b)) 'or' ('not' (a 'or' c))
let a, b, c be Function of Y,BOOLEAN; :: thesis: a 'nor' (b '&' c) = ('not' (a 'or' b)) 'or' ('not' (a 'or' c))
a 'nor' (b '&' c) = 'not' (a 'or' (b '&' c)) by Th2
.= 'not' ((a 'or' b) '&' (a 'or' c)) by BVFUNC_1:11 ;
hence a 'nor' (b '&' c) = ('not' (a 'or' b)) 'or' ('not' (a 'or' c)) by BVFUNC_1:14; :: thesis: verum