Nonempty Class has Members

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Let $A$ be a class.


$A \ne \varnothing \iff \exists x: x \in A$



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\(\displaystyle A \ne \varnothing\) \(\iff\) \(\displaystyle \neg \forall x: \left({x \in A \iff x \in \varnothing}\right)\) Definition of Class Equality
\(\displaystyle \) \(\iff\) \(\displaystyle \neg \forall x: \neg x \in A\) Definition of Empty Set
\(\displaystyle \) \(\iff\) \(\displaystyle \exists x: x \in A\) De Morgan's Laws (Predicate Logic)