If the joint density $f_{X_1,...,X_n}(x_1,...,x_n)$ is symmetric about the origin, does this imply that each marginal cdf $F_{X_i}(0)=1/2$?

If the joint density $f_{X_1,…,X_n}(x_1,…,x_n)$ is symmetric about the origin in the sense that for any $(x_1,…,x_n)$, it holds that

$f_{X_1,…,X_n}(x_1,…,x_n)=f_{X_1,…,X_n}(-x_1,…,-x_n)$

, does this imply that each marginal cdf satisfy $F_{X_i}(0)=1/2$?

Intuitively this seems true, as each marginal density will also be symmetric about the origin, which implies $F_{X_i}(0)=1/2$.