Does $X\sim B(Y1,\delta)$ first-order stochastically dominate(FSD) $W\sim B(Y0,\delta)$ when $Y1$ FSD $Y0$

Question

It is very straightforward to prove $X\sim Binomial(n+1,\delta)$ first-order stochastically dominate $W\sim Binomial(n,\delta)$. However, is it also true that $X\sim B(Y1,\delta)$ first-order stochastically dominate(FSD) $W\sim B(Y0,\delta)$ when $Y1$ first-order stochastically dominate $Y0$? That is, in the latter case, $Y1$ and $Y0$ are random variables.