Image of Fredholm Operator of Banach Spaces is Closed

Theorem
Let $\Bbb F \in \set {\R, \C}$.

Let $X, Y$ be Banach spaces over $\Bbb F$.

Let $T: U \to V$ be a Fredholm operator.

Let $\Img T$ be the image of $T$.

Then $\Img T$ is closed.