In Todorcevic's book "Partition Problems in Topology" I have found Proposition 8.4(c) saying that under OCA for any uncountable sets $X,Y$ of reals there exists a strictly increasing function $f:Z\to Y$ defined on an uncountable subset $Z$ of $X$.

This proposition implies that for any uncountable set $X\subset \mathbb R$ there exists a strictly increasing function $f:Z\to -X$ defined on an uncountable subset $Z\subset X$. Then the function $-f:Z\to X$ is stricly decreasing.

Therefore the PFA-theorem in OP holds under OCA.

In Todorcevic's book "Partition Problems in Topology" I have found Proposition 8.4(c) saying that under OCA for any uncountable sets $X,Y$ of reals there exists a strictly increasing function $f:Z\to Y$ defined on some uncountable subset $Z$ of $X$.

This proposition implies that for any uncountable set $X\subset \mathbb R$ there exists a strictly increasing function $f:Z\to -X$ defined on some uncountable subset $Z\subset X$. Then the function $-f:Z\to X$ is stricly decreasing.

Therefore the PFA-theorem in OP holds under OCA.