The phenomenon extends completely up the hyperarithmetic hierarchy and beyond, including analytic sentences, up into the [projective hiearchary](http://en.wikipedia.org/wiki/Projective_hierarchy) at the level of $\Sigma^1_2$. This is because the Shoenfield Absoluteness Theorem asserts that any $\Sigma^1_2$ statement is absolute between between any two models of set theory $V\subset W$ having the same ordinals. In particular, a $\Sigma^1_2$ statement holds in the universe if and only if it holds in the constructible universe $L$, where both AC and GCH hold. Thus, the $\Sigma^1_2$ statements provable in ZFC+GCH are the same as those provable in ZF.