let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds
( (a '&' b) '&' c '<' a & (a '&' b) '&' c '<' b )
let a, b, c be Function of Y,BOOLEAN; :: thesis: ( (a '&' b) '&' c '<' a & (a '&' b) '&' c '<' b )
( (a '&' b) '&' c = (c '&' b) '&' a & ((c '&' b) '&' a) 'imp' a = I_el Y ) by BVFUNC_1:4, Th38;
hence (a '&' b) '&' c '<' a by BVFUNC_1:16; :: thesis: (a '&' b) '&' c '<' b
( (a '&' b) '&' c = (a '&' c) '&' b & ((a '&' c) '&' b) 'imp' b = I_el Y ) by BVFUNC_1:4, Th38;
hence (a '&' b) '&' c '<' b by BVFUNC_1:16; :: thesis: verum