let Y be non empty set ; :: thesis: for a, b being Function of Y,BOOLEAN holds (a 'imp' b) 'or' (a 'imp' ('not' b)) = I_el Y
let a, b be Function of Y,BOOLEAN; :: thesis: (a 'imp' b) 'or' (a 'imp' ('not' b)) = I_el Y
(a 'imp' b) 'or' (a 'imp' ('not' b)) = (('not' a) 'or' b) 'or' (a 'imp' ('not' b)) by BVFUNC_4:8
.= (('not' a) 'or' b) 'or' (('not' a) 'or' ('not' b)) by BVFUNC_4:8
.= ('not' a) 'or' (b 'or' (('not' b) 'or' ('not' a))) by BVFUNC_1:8
.= ('not' a) 'or' ((b 'or' ('not' b)) 'or' ('not' a)) by BVFUNC_1:8
.= ('not' a) 'or' ((I_el Y) 'or' ('not' a)) by BVFUNC_4:6
.= ('not' a) 'or' (I_el Y) by BVFUNC_1:10 ;
hence (a 'imp' b) 'or' (a 'imp' ('not' b)) = I_el Y by BVFUNC_1:10; :: thesis: verum