let Y be non empty set ; :: thesis: for a, b, c being Function of Y,BOOLEAN holds ((a '&' ('not' b)) 'or' (b '&' ('not' c))) 'or' (c '&' ('not' a)) = ((b '&' ('not' a)) 'or' (c '&' ('not' b))) 'or' (a '&' ('not' c))
let a, b, c be Function of Y,BOOLEAN; :: thesis: ((a '&' ('not' b)) 'or' (b '&' ('not' c))) 'or' (c '&' ('not' a)) = ((b '&' ('not' a)) 'or' (c '&' ('not' b))) 'or' (a '&' ('not' c))
( ((a '&' ('not' b)) 'or' (b '&' ('not' c))) 'or' (c '&' ('not' a)) '<' ((b '&' ('not' a)) 'or' (c '&' ('not' b))) 'or' (a '&' ('not' c)) & ((b '&' ('not' a)) 'or' (c '&' ('not' b))) 'or' (a '&' ('not' c)) '<' ((a '&' ('not' b)) 'or' (b '&' ('not' c))) 'or' (c '&' ('not' a)) ) by Lm1;
hence ((a '&' ('not' b)) 'or' (b '&' ('not' c))) 'or' (c '&' ('not' a)) = ((b '&' ('not' a)) 'or' (c '&' ('not' b))) 'or' (a '&' ('not' c)) by BVFUNC_1:15; :: thesis: verum