I'm trying a problem which asks which axioms of ZFC hold - under the assumption that there exists a weakly inaccessible cardinal $\kappa$ - inside $V_{\kappa}$ ($\kappa$ being such a cardinal).
I am relatively sure I have argued that everything holds except replacement which I am struggling with. I don't seem to have used the weakly inaccessible cardinal part with the others, so I am guessing this is where it comes in, but I'm not even sure what I'm meant to be considering. If I take $x\in V_{\kappa}$ and consider some function defined on $x$, am I considering functions into $V_{\kappa}$ only? Even if this is the case, how do I use regularity of $\kappa$ to argue $f(x)\in V_{\kappa}?$