let p, q, r be boolean object ; :: thesis: p 'nor' (q '&' r) = ('not' (p 'or' q)) 'or' ('not' (p 'or' r))
( p = FALSE or p = TRUE ) by Def3;
hence p 'nor' (q '&' r) = ('not' (p 'or' q)) 'or' ('not' (p 'or' r)) ; :: thesis: verum