空集合の公理は置換公理から導出でき

証明

$ \forall\psi\forall X\exists A\forall x\left(x\in A\iff (x\in X\land\psi(x))\right)

$ \implies \forall X\exists A\forall x(x\in A\iff(x\in X\land\bot))

$ \iff \forall X\exists A\forall x(x\in A\iff\bot)

$ \iff \underline{\exists A\forall x(x\notin A)}_{\quad\blacksquare}

References