Theory of Computing ------------------- Title : A Simple Proof of Toda's Theorem Authors : Lance Fortnow Volume : 5 Number : 7 Pages : 135-140 URL : https://theoryofcomputing.org/articles/v005a007 Abstract -------- Toda in his celebrated paper showed that the polynomial-time hierarchy is contained in P^{#P}. We give a short and simple proof of the first half of Toda's theorem that the polynomial-time hierarchy is contained in P^{parity-P}. Our proof uses easy consequences of relativizable proofs of results that predate Toda. For completeness we also include a proof of the second half of Toda's theorem.