let Y be non empty set ; :: thesis: for a, b being Element of Funcs (Y,BOOLEAN) holds a 'nor' (a 'nand' b) = O_el Y
let a, b be Element of Funcs (Y,BOOLEAN); :: thesis: a 'nor' (a 'nand' b) = O_el Y
thus a 'nor' (a 'nand' b) = 'not' ((a 'or' ('not' a)) 'or' ('not' b)) by Th55
.= 'not' ((I_el Y) 'or' ('not' b)) by BVFUNC_4:6
.= 'not' (I_el Y) by BVFUNC_1:10
.= O_el Y by BVFUNC_1:2 ; :: thesis: verum