let Y be non empty set ; :: thesis: for a being Function of Y,BOOLEAN holds a 'eqv' ('not' a) = O_el Y
let a be Function of Y,BOOLEAN; :: thesis: a 'eqv' ('not' a) = O_el Y
thus a 'eqv' ('not' a) = (a 'imp' ('not' a)) '&' (('not' a) 'imp' a) by BVFUNC_4:7
.= (('not' a) 'or' ('not' a)) '&' (('not' a) 'imp' a) by BVFUNC_4:8
.= ('not' a) '&' (('not' ('not' a)) 'or' a) by BVFUNC_4:8
.= O_el Y by BVFUNC_4:5 ; :: thesis: verum