 Freiling axiom of symmetry

Every function $f:\mathbb{R}\to [\mathbb{R}{]}^{<{\omega }_1}$ has reals $x,y$ with $x\notin f(y)$ and $y\notin f(x)$. The values are countable subsets. Requiring distinct witnesses is equivalent, by first adjoining $x$ to $f(x)$. The Freiling theorem identifies this axiom with the negation of the Continuum hypothesis in ZFC.