Reference Request: Preservation of étale maps under rigid analytic GAGA

Question

Let $K$ be a finite extension of $\mathbb{Q}_p$. As the title says, I am looking for a reference in which it is shown that given an étale map $f:X\rightarrow Y$ between smooth algebraic $K$-varieties, the induced map $f:X^{an}\rightarrow Y^{an}$ is an étale morphism of smooth rigid spaces.

Answer 1

For rigid spaces, you can find a reference in Theorem 5.2.1, part 1 of Conrad's Irreducible components of rigid spaces. The statement for Berkovich spaces can be found in Proposition 3.4.6 of Berkovich's book. The statement for adic spaces can be deduced from the statement for rigid spaces and Proposition 1.7.11 in Huber's book. There is a probably a more direct reference for adic spaces in Huber's book.