Theorem nalset

Description: No set contains all sets. Theorem 41 of Suppes p. 30. (Contributed by NM, 23-Aug-1993) Extract exnelv . (Revised by Matthew House, 12-Apr-2026)

	Ref	Expression
Assertion	nalset	$$⊢\neg \exists x\forall yy\in x$$

Proof

Step	Hyp	Ref	Expression
1		alexn	$$⊢\forall x\exists y\neg y\in x\leftrightarrow \neg \exists x\forall yy\in x$$
2		exnelv	$$⊢\exists y\neg y\in x$$
3	1 2	mpgbi	$$⊢\neg \exists x\forall yy\in x$$