let Y be non empty set ; :: thesis: for a being Function of Y,BOOLEAN holds
( a 'nor' ('not' a) = O_el Y & 'not' (a 'nor' ('not' a)) = I_el Y )
let a be Function of Y,BOOLEAN; :: thesis: ( a 'nor' ('not' a) = O_el Y & 'not' (a 'nor' ('not' a)) = I_el Y )
a 'nor' ('not' a) = 'not' (a 'or' ('not' a)) by Th2
.= 'not' (I_el Y) by BVFUNC_4:6
.= O_el Y by BVFUNC_1:2 ;
hence ( a 'nor' ('not' a) = O_el Y & 'not' (a 'nor' ('not' a)) = I_el Y ) by BVFUNC_1:2; :: thesis: verum