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