let Y be non empty set ; :: thesis: for a1, a2, b1, b2 being Element of Funcs Y,BOOLEAN holds (((a1 'imp' b1) '&' (a2 'imp' b2)) '&' (a1 'or' a2)) '&' ('not' (b1 '&' b2)) = (((b1 'imp' a1) '&' (b2 'imp' a2)) '&' (b1 'or' b2)) '&' ('not' (a1 '&' a2))
let a1, a2, b1, b2 be Element of Funcs Y,BOOLEAN ; :: thesis: (((a1 'imp' b1) '&' (a2 'imp' b2)) '&' (a1 'or' a2)) '&' ('not' (b1 '&' b2)) = (((b1 'imp' a1) '&' (b2 'imp' a2)) '&' (b1 'or' b2)) '&' ('not' (a1 '&' a2))
A1: (((a1 'imp' b1) '&' (a2 'imp' b2)) '&' (a1 'or' a2)) '&' ('not' (b1 '&' b2)) '<' (((b1 'imp' a1) '&' (b2 'imp' a2)) '&' (b1 'or' b2)) '&' ('not' (a1 '&' a2)) by Lm3;
(((b1 'imp' a1) '&' (b2 'imp' a2)) '&' (b1 'or' b2)) '&' ('not' (a1 '&' a2)) '<' (((a1 'imp' b1) '&' (a2 'imp' b2)) '&' (a1 'or' a2)) '&' ('not' (b1 '&' b2)) by Lm3;
hence (((a1 'imp' b1) '&' (a2 'imp' b2)) '&' (a1 'or' a2)) '&' ('not' (b1 '&' b2)) = (((b1 'imp' a1) '&' (b2 'imp' a2)) '&' (b1 'or' b2)) '&' ('not' (a1 '&' a2)) by A1, BVFUNC_1:18; :: thesis: verum