let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds ((a 'imp' b) '&' (a '&' c)) 'imp' (b '&' c) = I_el Y
let a, b, c be Function of Y,BOOLEAN; :: thesis: ((a 'imp' b) '&' (a '&' c)) 'imp' (b '&' c) = I_el Y
((a 'imp' b) '&' (a '&' c)) 'imp' (b '&' c) = (((a 'imp' b) '&' a) '&' c) 'imp' (b '&' c) by BVFUNC_1:4
.= ((a '&' b) '&' c) 'imp' (b '&' c) by BVFUNC_6:56
.= (a '&' (b '&' c)) 'imp' (b '&' c) by BVFUNC_1:4 ;
hence ((a 'imp' b) '&' (a '&' c)) 'imp' (b '&' c) = I_el Y by BVFUNC_6:38; :: thesis: verum