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	|- -. E. x A. y y e. x

Proof

Step	Hyp	Ref	Expression
1		alexn	|- ( A. x E. y -. y e. x <-> -. E. x A. y y e. x )
2		exnelv	|- E. y -. y e. x
3	1 2	mpgbi	|- -. E. x A. y y e. x