let Y be non empty set ; for a, b, c being Function of Y,BOOLEAN holds (a 'imp' b) '&' (b 'imp' c) '<' (a 'imp' (b 'or' ('not' c))) '&' (b 'imp' (c 'or' ('not' a)))
let a, b, c be Function of Y,BOOLEAN; (a 'imp' b) '&' (b 'imp' c) '<' (a 'imp' (b 'or' ('not' c))) '&' (b 'imp' (c 'or' ('not' a)))
(a 'imp' b) '&' (b 'imp' c) '<' b 'imp' (c 'or' ('not' a))
by Th22;
then A1:
((a 'imp' b) '&' (b 'imp' c)) 'imp' (b 'imp' (c 'or' ('not' a))) = I_el Y
by BVFUNC_1:16;
(a 'imp' b) '&' (b 'imp' c) '<' a 'imp' (b 'or' ('not' c))
by Th20;
then
((a 'imp' b) '&' (b 'imp' c)) 'imp' (a 'imp' (b 'or' ('not' c))) = I_el Y
by BVFUNC_1:16;
then
((a 'imp' b) '&' (b 'imp' c)) 'imp' ((a 'imp' (b 'or' ('not' c))) '&' (b 'imp' (c 'or' ('not' a)))) = I_el Y
by A1, th18;
hence
(a 'imp' b) '&' (b 'imp' c) '<' (a 'imp' (b 'or' ('not' c))) '&' (b 'imp' (c 'or' ('not' a)))
by BVFUNC_1:16; verum