let p, q, r be boolean object ; :: thesis: p 'or' (q '&' r) = (p 'or' q) '&' (p 'or' r)
( p = FALSE or p = TRUE ) by Def3;
hence p 'or' (q '&' r) = (p 'or' q) '&' (p 'or' r) ; :: thesis: verum