for x, y, z being Element of BOOLEAN holds
( and3 . <*x,y,z*> = (x '&' y) '&' z & and3a . <*x,y,z*> = (('not' x) '&' y) '&' z & and3b . <*x,y,z*> = (('not' x) '&' ('not' y)) '&' z & nor3 . <*x,y,z*> = (('not' x) '&' ('not' y)) '&' ('not' z) ) by Def9, Def10, Def11, Lm7;