let Y be non empty set ; :: thesis: for a, b, c being Element of Funcs 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 Element of Funcs 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))
A1: ((a '&' ('not' b)) 'or' (b '&' ('not' c))) 'or' (c '&' ('not' a)) '<' ((b '&' ('not' a)) 'or' (c '&' ('not' b))) 'or' (a '&' ('not' c)) by Lm1;
((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 A1, BVFUNC_1:18; :: thesis: verum