Axiom of foundation

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$\newcommand{\limplies}[0]{\rightarrow}$

Definition

• $\forall S\big[S\neq\emptyset\limplies\exists x[x\in S\wedge S\cap x\eq\emptyset]\big]$
  • In words:
    • i.e. every non-empty set has an $\in$-minimal element