reserve Y for non empty set,
  a,b,c,d for Function of Y,BOOLEAN;
reserve Y for non empty set,
  a,b,c for Function of Y,BOOLEAN;

theorem Th52:
  a 'xor' (b 'nand' c) = ('not' a '&' 'not' (b '&' c)) 'or' (a '&' b '&' c)
proof
  thus a 'xor' (b 'nand' c) =a 'xor' 'not' (b '&' c) by th1
    .=('not' a '&' 'not' (b '&' c)) 'or' (a '&' 'not' 'not' (b '&' c)) by
BVFUNC_4:9
    .=('not' a '&' 'not' (b '&' c)) 'or' (a '&' b '&' c) by BVFUNC_1:4;
end;
