let Y be non empty set ; :: thesis: for a being Function of Y,BOOLEAN holds a 'xor' a = O_el Y
let a be Function of Y,BOOLEAN; :: thesis: a 'xor' a = O_el Y
thus a 'xor' a = (('not' a) '&' a) 'or' (a '&' ('not' a)) by BVFUNC_4:9
.= O_el Y by BVFUNC_4:5 ; :: thesis: verum