let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'imp' b = a 'imp' (a '&' b)
let a, b be Function of Y,BOOLEAN; :: thesis: a 'imp' b = a 'imp' (a '&' b)
a 'imp' (a '&' b) = ('not' a) 'or' (a '&' b) by BVFUNC_4:8
.= (('not' a) 'or' a) '&' (('not' a) 'or' b) by BVFUNC_1:11
.= (I_el Y) '&' (('not' a) 'or' b) by BVFUNC_4:6
.= ('not' a) 'or' b by BVFUNC_1:6 ;
hence a 'imp' b = a 'imp' (a '&' b) by BVFUNC_4:8; :: thesis: verum