We have defined the set $\omega$ as minimal with respect to the inclusion "$\in$" in relation to all inductive sets. The following corollary states that $\omega$ is also minimal, if we look at that relation of being the subset $\subseteq$ of inductive sets:# Corollary: Minimal Inductive Set Is Subset Of All Inductive Sets
(related to Axiom: Axiom of Infinity)
The minimal inductive set $\omega$ is a subset of all inductive sets, formally: $$\forall W(W\text{ is inductive }\Rightarrow \omega\subseteq W).$$
Proofs: 1
Explanations: 1