let Y be non empty set ; :: thesis: ( (O_el Y) 'nand' (O_el Y) = I_el Y & (O_el Y) 'nand' (I_el Y) = I_el Y & (I_el Y) 'nand' (I_el Y) = O_el Y )
thus (O_el Y) 'nand' (O_el Y) = I_el Y by Th4; :: thesis: ( (O_el Y) 'nand' (I_el Y) = I_el Y & (I_el Y) 'nand' (I_el Y) = O_el Y )
thus (O_el Y) 'nand' (I_el Y) = I_el Y by Th4; :: thesis: (I_el Y) 'nand' (I_el Y) = O_el Y
thus (I_el Y) 'nand' (I_el Y) = 'not' (I_el Y) by Th3
.= O_el Y by BVFUNC_1:2 ; :: thesis: verum