let p, q, r be boolean number ; :: thesis: p 'or' (q <=> r) = ((p 'or' ('not' q)) 'or' r) '&' ((p 'or' ('not' r)) 'or' q)
( p = FALSE or p = TRUE ) by Def3;
hence p 'or' (q <=> r) = ((p 'or' ('not' q)) 'or' r) '&' ((p 'or' ('not' r)) 'or' q) ; :: thesis: verum