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
  a 'nand' (b 'nor' c) = 'not' a 'or' b 'or' c & a 'nand' (b 'nor' c) =
  a 'imp' (b 'or' c)
proof
A1: a 'nand' (b 'nor' c) = 'not' (a '&' (b 'nor' c)) by th1
    .= 'not' (a '&' 'not' (b 'or' c)) by Th2
    .= 'not' a 'or' 'not' 'not' (b 'or' c) by BVFUNC_1:14
    .= 'not' a 'or' b 'or' c by BVFUNC_1:8;
  then a 'nand' (b 'nor' c) = 'not' a 'or' (b 'or' c) by BVFUNC_1:8;
  hence thesis by A1,BVFUNC_4:8;
end;
