let Y be non empty set ; :: thesis: for a being Element of Funcs Y,BOOLEAN holds (I_el Y) 'nand' a = 'not' a
let a be Element of Funcs Y,BOOLEAN ; :: thesis: (I_el Y) 'nand' a = 'not' a
(I_el Y) 'nand' a = 'not' ((I_el Y) '&' a) by Th1;
hence (I_el Y) 'nand' a = 'not' a by BVFUNC_1:9; :: thesis: verum