Axiom of Infinity

$$\begin{array}{r}0:=\varnothing \\ s(x):=x\cup \{x\}\\ I(S)⟺0\in S\wedge \forall x\in S.s(x)\in S\\ \exists S:Set.I(S)\\ \mathbb{N}=\{x.\forall S:I.x\in S\}\end{array}$$