Reflection implies the SCH

We prove that, e.g., if $\mu > \mathop{\rm cf}\nolimits(\mu) = \aleph_0$ and $\mu > 2^{\aleph_0}$ and every stationary family of countable subsets of $\mu^+$ reflects in some subset of $\mu^+$ of cardinality $\aleph_1$, then the SCH for $\mu^+$ holds (mor