let Y be non empty set ; :: thesis: for a, b being Element of Funcs (Y,BOOLEAN) holds a '&' (a 'nor' b) = O_el Y
let a, b be Element of Funcs (Y,BOOLEAN); :: thesis: a '&' (a 'nor' b) = O_el Y
thus a '&' (a 'nor' b) = (a '&' ('not' a)) '&' ('not' b) by Th62
.= (O_el Y) '&' ('not' b) by BVFUNC_4:5
.= O_el Y by BVFUNC_1:5 ; :: thesis: verum