A known PFA-results of Baumgartner (about the order isomorphness of any $\aleph_1$-dense subsets of the real line) has the following

Corollary. Under PFA, for any uncountable subset $X\subset\mathbb R$ there exists a strictly decreasing function $f:Z\to X$, defined on an uncountable subset $Z\subset X$.

Now

Question. What happens with this PFA-corollary in ZFC? Is it still true? Maybe it remains true under some weaker axioms like OCA or MA? Is it true under CH?