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