From wikipedia: http://en.wikipedia.org/wiki/Absoluteness#Shoenfield.27s_absoluteness_theorem

"Shoenfield's theorem shows that if there is a model ZF in which a given $\Pi^1_3$ statement $\phi$ is false, then $\phi$ is also false in the constructible universe of that model."

The problem is that the only proofs I can find seem to use "a model of ZF+DC" or "a model of ZFC".

Is wikipedia right? If so, is there a proof from just "a model of ZF" online or short enough to sketch here?