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