Is the pdf of chi-squared distribution increasing with smaller degrees of freedom?

Question

Proposition:

Consider $W_k \sim \chi^2(r(k))$, and then we derive $$Pr(W_k < t) \geq Pr(W_{s_n} < t),$$

where $k$ and $s_n$ are the degrees of freedom, and $k \leq s_n$.

How to prove it?