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

Theorem. 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. Can this PFA-theorem be proved under a weaker assumption like OCA or (MA$+\neg$ CH)? What happens with this theorem under CH or $\Diamond$?