let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a = (b 'imp' a) '&' (('not' b) 'imp' a)
let a, b be Function of Y,BOOLEAN; :: thesis: a = (b 'imp' a) '&' (('not' b) 'imp' a)
a = (a 'or' b) '&' (a 'or' ('not' b)) by BVFUNC_6:80
.= (a 'or' ('not' ('not' b))) '&' (b 'imp' a) by BVFUNC_4:8
.= (('not' b) 'imp' a) '&' (b 'imp' a) by BVFUNC_4:8 ;
hence a = (b 'imp' a) '&' (('not' b) 'imp' a) ; :: thesis: verum