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