Proof that if P=PSPACE, RP=BPP

Question

Like the title says. I can't figure out how to prove this.

I think it probably has to do with the polynomial hierarchy collapsing but I'm not sure.

Answer 1

$P \subseteq RP $, $BPP \subseteq PSPACE $.

So $PSPACE \subseteq P $, $-->$ $BPP \subseteq RP $.