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