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 Th37:
  a 'nor' (b 'nand' c) = 'not' a '&' b '&' c
proof
  thus a 'nor' (b 'nand' c) = 'not' (a 'or' (b 'nand' c)) by Th2
    .= 'not' (a 'or' 'not' (b '&' c)) by th1
    .= 'not' a '&' 'not' 'not' (b '&' c) by BVFUNC_1:13
    .= 'not' a '&' b '&' c by BVFUNC_1:4;
end;
