Axiom of Foundation (Strong Form)/Proof 1

Proof
By Epsilon Relation is Strictly Well-Founded, $\Epsilon$, the epsilon relation, is a strictly well-founded relation on $B$.

By Epsilon Relation is Proper, $\struct {\mathbb U, \Epsilon}$ is a proper relational structure, where $\mathbb U$ is the universal class.

By Well-Founded Proper Relational Structure Determines Minimal Elements, $B$ has an $\Epsilon$-minimal element.