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Metamath Proof Explorer

Theorem prsnex

Description: The class of preordered sets is a proper class. (Contributed by Zhi Wang, 20-Oct-2025)

		Ref	Expression
	Assertion	prsnex	$⊢ Proset \notin V$

Step	Hyp	Ref	Expression
1		vprc	$⊢ \neg V \in V$
2	1	nelir	$⊢ V \notin V$
3		basresprsfo	$⊢ ({Base ↾}_{Proset}) : Proset \underset{onto}{⟶} V$
4	2 3	fonex	$⊢ Proset \notin V$