let Y be non empty set ; :: thesis: for a being Function of Y,BOOLEAN holds
( a 'nor' a = 'not' a & 'not' (a 'nor' a) = a )
let a be Function of Y,BOOLEAN; :: thesis: ( a 'nor' a = 'not' a & 'not' (a 'nor' a) = a )
a 'nor' a = 'not' (a 'or' a) by Th2
.= 'not' a ;
hence ( a 'nor' a = 'not' a & 'not' (a 'nor' a) = a ) ; :: thesis: verum