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