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