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Metamath Proof Explorer

Theorem vsn

Description: The singleton of the universal class is the empty set. (Contributed by Zhi Wang, 19-Sep-2024)

		Ref	Expression
	Assertion	vsn	$⊢ \{V\} = \emptyset$

Step	Hyp	Ref	Expression
1		vprc	$⊢ \neg V \in V$
2		snprc	$⊢ \neg V \in V \leftrightarrow \{V\} = \emptyset$
3	1 2	mpbi	$⊢ \{V\} = \emptyset$