let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds a 'or' b = (a 'imp' b) 'imp' b
let a, b be Function of Y,BOOLEAN; :: thesis: a 'or' b = (a 'imp' b) 'imp' b
thus (a 'imp' b) 'imp' b = ('not' (a 'imp' b)) 'or' b by BVFUNC_4:8
.= ('not' (('not' a) 'or' b)) 'or' b by BVFUNC_4:8
.= (('not' ('not' a)) '&' ('not' b)) 'or' b by BVFUNC_1:13
.= (a 'or' b) '&' (('not' b) 'or' b) by BVFUNC_1:11
.= (a 'or' b) '&' (I_el Y) by BVFUNC_4:6
.= a 'or' b by BVFUNC_1:6 ; :: thesis: verum