theorem
  Valid('not' 'not' p,J) = Valid(p,J)
proof
  now
    let v;
    thus Valid('not' 'not' p,J).v = 'not'(Valid('not' p,J).v) by Th10
      .= 'not'('not'(Valid(p,J).v)) by Th10
      .= Valid(p,J).v;
  end;
  hence thesis by FUNCT_2:63;
end;
