let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds (a 'imp' b) '&' (b 'imp' c) '<' (a 'imp' b) '&' (b 'imp' (c 'or' a))
let a, b, c be Function of Y,BOOLEAN; :: thesis: (a 'imp' b) '&' (b 'imp' c) '<' (a 'imp' b) '&' (b 'imp' (c 'or' a))
(a 'imp' b) '&' (b 'imp' c) '<' b 'imp' (c 'or' a) by Th21;
then A1: ((a 'imp' b) '&' (b 'imp' c)) 'imp' (b 'imp' (c 'or' a)) = I_el Y by BVFUNC_1:16;
((a 'imp' b) '&' (b 'imp' c)) 'imp' (a 'imp' b) = I_el Y by Th38;
then ((a 'imp' b) '&' (b 'imp' c)) 'imp' ((a 'imp' b) '&' (b 'imp' (c 'or' a))) = I_el Y by A1, th18;
hence (a 'imp' b) '&' (b 'imp' c) '<' (a 'imp' b) '&' (b 'imp' (c 'or' a)) by BVFUNC_1:16; :: thesis: verum