let Y be non empty set ; :: thesis: for a being Function of Y,BOOLEAN holds
( a 'nand' ('not' a) = I_el Y & 'not' (a 'nand' ('not' a)) = O_el Y )
let a be Function of Y,BOOLEAN; :: thesis: ( a 'nand' ('not' a) = I_el Y & 'not' (a 'nand' ('not' a)) = O_el Y )
a 'nand' ('not' a) = 'not' (a '&' ('not' a)) by th1
.= 'not' (O_el Y) by BVFUNC_4:5
.= I_el Y by BVFUNC_1:2 ;
hence ( a 'nand' ('not' a) = I_el Y & 'not' (a 'nand' ('not' a)) = O_el Y ) by BVFUNC_1:2; :: thesis: verum