Wikipedia article on Baire category theorem and several other sources mention this paper: Blair, Charles E. The Baire category theorem implies the principle of dependent choices. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 25 (1977), no. 10, 933–934. MR0469765, Zbl 0377.04011. However, I did not succeed in finding this paper online.
Still you can find this result for example in:
- Horst Herrlich: Axiom of Choice as Theorem 4.106
- Theo Bühler, Dietmar A. Salamon: Functional Analysis as Exercise 1.7.14
I will freely admit that I found the above results simply by trying to search for some suitable phrases in Google Books and Google Scholar. Maybe you might find some further references in this way. It might be also worth checking the work which cite the Blair's paper, you can try them, e.g., in Google Scholar, Zentralblatt or MathSciNet. (I do not have access to the latter.)