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