I have a problem to proof this theorem, Anyone can help for detail.

"A subspace of Banach space is complete if and only if is closed in "

I have an idea to prove this theorem, but I am not sure about this and I can't wrote it for detail.

Please correct my answer,

from left to right "let is Banach space, . so, is Banach space. consider of Banach space definition, every Cauchy sequence of is converge to then is closed on ".

right to left "I am still totally confuse..."