If you trust base system B, then a proof that P is provable in B is good as gold to you. But it is not a proof in B.
http://lesswrong.com/lw/t6/the_cartoon_guide_to_l%C3%B6bs_theorem/
If you trust base system B, then a proof that P is provable in B is good as gold to you. But it is not a proof in B.
http://lesswrong.com/lw/t6/the_cartoon_guide_to_l%C3%B6bs_theorem/