This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem posnex

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

		Ref	Expression
	Assertion	posnex	$⊢ Poset \notin V$

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